Latest in math.dg

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Stability of Ricci de Turck flow on Singular SpacesFeb 08 2018In this paper we establish stability of the Ricci de Turck flow near Ricci-flat metrics with isolated conical singularities. More precisely, we construct a Ricci de Turck flow which starts sufficiently close to a Ricci-flat metric with isolated conical ... More
Positivity and higher Teichmüller theoryFeb 08 2018We introduce $\Theta$-positivity, a new notion of positivity in real semisimple Lie groups. The notion of $\Theta$-positivity generalizes at the same time Lusztig's total positivity in split real Lie groups as well as well known concepts of positivity ... More
Average number of zeros and mixed symplectic volume of Finsler setsFeb 08 2018Let $X$ be an $n$-dimensional manifold and $V_1, \ldots, V_n \subset C^\infty(X, \mathbb R)$ finite-dimensional vector spaces with Euclidean metric. We assign to each $V_i$ a Finsler ellipsoid, i.e., a family of ellipsoids in the fibers of the cotangent ... More
Representation and Characterization of Non-Stationary Processes by Dilation Operators and Induced Shape Space ManifoldsFeb 08 2018We have introduce a new vision of stochastic processes through the geometry induced by the dilation. The dilation matrices of a given processes are obtained by a composition of rotations matrices, contain the measure information in a condensed way. Particularly ... More
The nullity of homogeneous Riemannian manifolsFeb 07 2018In this paper we study the nullity distribution $\nu$, of the Riemannian curvature tensor $R$, of a homogeneous Riemannian manifold $M=G/H$. If $M$ is compact, $\nu$ is parallel and so $M$ locally splits off a flat factor if $\nu \neq 0$. We introduce ... More
The monodromy of meromorphic projective structuresFeb 07 2018We study projective structures on a surface having poles of prescribed orders. We obtain a monodromy map from a complex manifold parameterising such structures to the stack of framed $\mathrm{PGL}_2(\mathbb{C})$ local systems on the associated marked ... More
Asymptotically Locally Euclidean/Kaluza-Klein Stationary Vacuum Black Holes in 5 DimensionsFeb 07 2018We produce new examples, both explicit and analytical, of bi-axisymmetric stationary vacuum black holes in 5 dimensions. A novel feature of these solutions is that they are asymptotically locally Euclidean in which spatial cross-sections at infinity have ... More
A Novel Supergeometric Generalization of GrassmanniansFeb 07 2018A new generalization of Grassmannians to supergeometry, different from the well known supergrassmannian, is introduced. These are constructed by gluing a finite number of copies of a \nu\- domain, i.e. a superdomain with an odd involution, say \nu\, on ... More
Semi Concurrent vector fields in Finsler geometryFeb 07 2018In the present paper, we introduce and investigate the notion of a semi concurrent vector field on a Finsler manifold. We show that some special Finsler manifolds admitting such vector fields turn out to be Riemannian. We prove that Tachibana's characterization ... More
Complete Lagrangian self-shrinkers in $\mathbf R^4$Feb 07 2018It is our purpose to study complete self-shrinkers of mean curvature flow in Euclidean spaces. We give a complete classification for 2-dimensional complete Lagrangian self-shrinkers in Euclidean space $\mathbb R^4$ with constant squared norm of the second ... More
The equivariant cohomology ring of a cohomogeneity-one actionFeb 07 2018We compute the rational Borel equivariant cohomology ring of a cohomogeneity-one action of a compact Lie group.
Nullity of the Levi-form and the associated subvarieties for pseudo-convex CR structures of hypersurface typeFeb 07 2018Let $M^{2n+1}$, $n\ge 1$, be a smooth manifold with a pseudo-convex integrable CR structure of hypersurface type. We consider a sequence of CR invariant subsets $ M=\mathcal S_0 \supset \mathcal S_1 \supset \cdots \supset \mathcal S_{n}, $ where $\mathcal ... More
A note on the evolution of the Whitney sphere along mean curvature flowFeb 06 2018We study the evolution of the Whitney sphere along the Lagrangian mean curvature flow. We show that equivariant Lagrangian spheres in $\mathbb{C}^n$ satisfying mild geometric assumptions collapse to a point in finite time and the tangent flows converge ... More
Complete complex hypersurfaces in the ball come in nonsingular foliationsFeb 06 2018In this paper we prove that every smooth complete closed complex hypersurface in the open unit ball $\mathbb{B}_n$ of $\mathbb{C}^n$ $(n\ge 2)$ is a level set of a noncritical holomorphic function on $\mathbb{B}_n$ all of whose level sets are complete. ... More
A Note On Conformal Vector Fields Of $(α,β)$-SpacesFeb 06 2018In this paper, we characterize conformal vector fields of any (regular or singular) $(\alpha,\beta)$-space with some PDEs. Further, we show some properties of conformal vector fields of a class of singular $(\alpha,\beta)$-spaces satisfying certain geometric ... More
Remarks on the self-shrinking Clifford torusFeb 05 2018On the one hand, we prove that the Clifford torus in $\mathbb{C}^2$ is unstable for Lagrangian mean curvature flow under arbitrarily small Hamiltonian perturbations, even though it is Hamiltonian $F$-stable and locally area minimising under Hamiltonian ... More
On homogeneous geodesics and weakly symmetric spacesFeb 04 2018In this paper, we establish a sufficient condition for a geodesic in a Riemannian manifold to be homogeneous, i.e. an orbit of an $1$-parameter isometry group. As an application of this result, we provide a new proof of the fact that every weakly symmetric ... More
Vector Hamiltonians in Nambu mechanicsFeb 03 2018We give a generalization of the Nambu mechanics based on vector Hamiltonians theory. It is shown that any divergence-free phase flow in $\mathbb{R}^n$ can be represented as a generalized Nambu mechanics with $n-1$ integral invariants. For the case when ... More
Regularity and quantitative gradient estimate of p-harmonic mappings between Riemannian manifoldsFeb 03 2018Let $M$ be a $C^2$-smooth Riemannian manifold with boundary and $N$ a complete $C^2$-smooth Riemannian manifold. We show that each minimizing $p$-harmonic mapping $u\colon M\to N$ is locally $C^{1,\alpha}$ for some $\alpha\in (0,1)$, provided either $N$ ... More
Small sphere limit of the quasi-local energy with anti de-Sitter space referenceFeb 02 2018In [13], a new quasi-local energy is introduced for spacetimes with a non-zero cosmological constant. In this article, we study the small sphere limit of this newly defined quasi-local energy for spacetimes with a negative cosmological constant. For such ... More
Differential invariants of Einstein-Weyl structures in 3DFeb 02 2018Einstein-Weyl structures on a three-dimensional manifold $M$ is given by a system $E$ of PDEs on sections of a bundle over $M$. This system is invariant under the Lie pseudogroup $G$ of local diffeomorphisms on $M$. Two Einstein-Weyl structures are locally ... More
Stable CMC integral varifolds of codimension $1$: regularity and compactnessFeb 01 2018We give two structural conditions on a codimension $1$ integral $n$-varifold with first variation locally summable to an exponent $p>n$ that imply the following: whenever each orientable portion of the $C^{1}$-embedded part of the varifold (which is non-empty ... More
Optimal isoperimetric inequalities for surfaces in any codimension in Cartan-Hadamard manifoldsFeb 01 2018Let $(M^n,g)$ be simply connected, complete, with non-positive sectional curvatures, and $\Sigma$ a 2-dimensional closed integral current (or flat chain mod 2) with compact support in $M$. Let $S$ be an area minimising integral 3-current (resp.~flat chain ... More
Geometric flow of high codimensionFeb 01 2018Feb 07 2018We consider the negative gradient flow associated to the following functional \[ \mathcal{F}_k(\varphi)=\int_M(1+|\bar{\nabla}^k\bar{\rho}|^2)\,d\mu. \] The functional is defined on immersion $\varphi:M\longrightarrow\mathbb{R}^n$, where $M$ is a $m$-dimensional ... More
Geometric flow of high orderFeb 01 2018We consider the negative gradient flow $\varphi:M\times[0,T)\longrightarrow N$($[0,T)$ is its maximal existence interval), taking $\varphi_0\in C^{\infty}(M,N)$ which is a immersion as its initial value, associated to the following functional \[ \mathfrak{F}_m(\Phi):=\int_M(1+|\dot{\nabla}^m\Upsilon|^2)\,d\mu, ... More
Geometry of extended Bianchi-Cartan-Vranceanu spacesJan 31 2018The differential geometry of $3$-dimensional Bianchi, Cartan and Vranceanu ($BCV$) spaces is well known. We introduce the extended Bianchi, Cartan and Vranceanu ($EBCV$) spaces as a natural seven dimensional generalization of $BCV$ spaces and study some ... More
On the Lichnerowicz conjecture for CR manifolds with mixed signatureJan 31 2018We construct examples of nondegenerate CR manifolds with Levi form of signature $(p,q)$, $2\leq p\leq q$, which are compact, not locally CR flat, and admit essential CR vector fields. We also construct an example of a noncompact nondegenerate CR manifold ... More
Error estimates for spectral convergence of the graph Laplacian on random geometric graphs towards the Laplace--Beltrami operatorJan 30 2018We study the convergence of the graph Laplacian of a random geometric graph generated by an i.i.d. sample from a $m$-dimensional submanifold $M$ in $R^d$ as the sample size $n$ increases and the neighborhood size $h$ tends to zero. We show that eigenvalues ... More
Deformation Cohomology of Lie Algebroids and Morita EquivalenceJan 30 2018Let $A \Rightarrow M$ be a Lie algebroid. In this short note we prove that a pull-back of $A$ along a fibration with homologically $k$-connected fibers, shares the same deformation cohomology of $A$ up to degree $k$.
Almost cosymplectic statistical manifoldsJan 30 2018This paper is a study of almost contact statistical manifolds. Especially this study is focused on almost cosymplectic statistical manifolds. We obtained basic properties of such manifolds. It is proved a characterization theorem and a corollary for the ... More
Positivity preserving along a flow over projective bundleJan 30 2018In this paper, we introduce a flow over the projective bundle $p:P(E^*)\to M$, which is a natural generalization of both Hermitian-Yang-Mills flow and K\"ahler-Ricci flow. We prove that the semipositivity of curvature of the hyperplane line bundle $\mathcal{O}_{P(E^*)}(1)$ ... More
A brief survey on singularities of geodesic flows in smooth signature changing metrics on 2-surfacesJan 30 2018We present a survey on generic singularities of geodesic flows in smooth signature changing metrics (often called pseudo-Riemannian) in dimension 2. Generically, a pseudo-Riemannian metric on a 2-manifold $S$ changes its signature (degenerates) along ... More
On Bott-Morse Foliations and their Poisson Structures in Dimension 3Jan 29 2018We show that a Bott-Morse foliation in dimension 3 admits a linear, singular, Poisson structure of rank 2 with Bott-Morse singularities. We provide the Poisson bivectors for each type of singular component, and compute the symplectic forms of the characteristic ... More
The Kähler geometry of Bott manifoldsJan 29 2018We study the K\"ahler geometry of stage n Bott manifolds, which can be viewed as $n$-dimensional generalizations of Hirzebruch surfaces. We show, using a simple induction argument and the generalized Calabi construction from [ACGT04,ACGT11], that any ... More
The point equivalence problem for ordinary differential equations of the second orderJan 28 2018We use E. Cartan's method to solve the problem of equivalence of the second order ordinary differential equations with respect to the pseudogroup of point transformations.
Rigidity of minimal submanifolds in space formsJan 26 2018In this paper, we consider the rigidity for an $n(\geq 4)$-dimensional submanfolds $M^n$ with parallel mean curvature in the space form ${\mathbb M}^{n+p}_c$ when the integral Ricci curvature of $M$ has some bound. We prove that, if $c+H^2>0$ and $\|\mathrm{Ric}_{-}^\lambda\|_{n/2}< ... More
On a class of immersions of spheres into space forms of nonpositive curvatureJan 25 2018Let $ J $ be an interval and $ M^{n+1} $ be a simply-connected space form of curvature $ -\kappa $, where $ \kappa \geq 0$. If $ J \subset [-\kappa,\kappa] $, then no closed $ n $-manifold can be immersed in $ M $ subject to the restriction that the principal ... More
Discrete projective minimal surfacesJan 25 2018We propose a natural discretisation scheme for classical projective minimal surfaces. We follow the classical geometric characterisation and classification of projective minimal surfaces and introduce at each step canonical discrete models of the associated ... More
Surface theory in discrete projective differential geometry. I. A canonical frame and an integrable discrete Demoulin systemJan 25 2018We present the first steps of a procedure which discretises surface theory in classical projective differential geometry in such a manner that underlying integrable structure is preserved. We propose a canonical frame in terms of which the associated ... More
Affine surfaces which are Kähler, para-Kähler, or nilpotent KählerJan 25 2018Motivated by the construction of Bach flat neutral signature Riemannian extensions, we study the space of parallel trace free tensors of type $(1,1)$ on an affine surface. It is shown that the existence of such a parallel tensor field is characterized ... More
Stability of nonnegative isotropic curvature under continuous deformations of the metricJan 25 2018Using a method introduced by R. Bamler to study the behavior of scalar curvature under continuous deformations of Riemannian metrics, we prove that if a sequence of smooth Riemannian metrics gi on a fixed compact manifold M has isotropic curvature bounded ... More
On the three-circle theorem and its applications in Sasakian manifoldsJan 25 2018Jan 30 2018This paper mainly focuses on the CR analogue of the three-circle theorem in a complete noncompact pseudohermitian manifold of vanishing torsion being odd dimensional counterpart of K\"ahler geometry. In this paper, we show that the CR three-circle theorem ... More
On Uniqueness And Existence of Conformally Compact Einstein Metrics with Homogeneous Conformal Infinity. IIJan 24 2018In this paper we show that for an $\text{Sp}(k+1)$ invariant metric $\hat{g}$ on $\mathbb{S}^{4k+3}$ $(k\geq 1)$ close to the round metric, the conformally compact Einstein (CCE) manifold $(M, g)$ with $(\mathbb{S}^{4k+3}, [\hat{g}])$ as its conformal ... More
A counterexample to Matsumoto's conjecture regarding absolute length vs. relative length in Finsler manifoldsJan 24 2018Matsumoto conjectured that for any Finsler manifold $(M, F)$ for which the restriction of the fundamental tensor to the indicatrix of $F$ is positive definite, the absolute length $F(X)$ of any tangent vector $X \in T_xM$ is the global minimum for the ... More
On Calabi's extremal metric and propernessJan 23 2018In this paper we extend recent breakthrough of Chen-Cheng \cite{CC1, CC2, CC3} on existence of constant scalar K\"ahler metric on a compact K\"ahler manifold to Calabi's extremal metric. Our argument follows \cite{CC3} and there are no new a prior estimates ... More
On the sharp dimension estimate of CR holomorphic functions in Sasakian ManifoldsJan 23 2018This is the very first paper to focus on the CR analogue of Yau's uniformization conjecture in a complete noncompact pseudohermitian $(2n+1)$-manifold of vanishing torsion (i.e. Sasakian manifold) which is an odd dimensional counterpart of K\"{a}hler ... More
C-projective symmetries of submanifolds in quaternionic geometryJan 22 2018The generalized Feix--Kaledin construction shows that c-projective $2n$-manifolds with curvature of type $(1,1)$ are precisely the submanifolds of quaternionic $4n$-manifolds which are fixed points set of a special type of quaternionic $S^1$ action $v$. ... More
Euclidean submanifolds with incompressible canonical vector fieldJan 22 2018Jan 29 2018For a submanifold M in a Euclidean space, the tangential component x^T of the position vector field x of M is the most natural vector field tangent to the Euclidean submanifold, called the canonical vector field of M. In this article, first we prove that ... More
New variational and multisymplectic formulations of the Euler-Poincaré equation on the Virasoro-Bott group using the inverse mapJan 22 2018Jan 25 2018We derive a new variational principle, leading to a new momentum map and a new multisymplectic formulation for a family of Euler--Poincar\'e equations defined on the Virasoro-Bott group, by using the inverse map (also called `back-to-labels' map). This ... More
Expressing the curvature tensor and connection of a given metric in terms of those of another metricJan 22 2018Let $(M,g)$ be a Riemannian manifold, and $m$ be a second metric on $M$. We give expressions of $m$'s associated connection, and Riemann curvature tensor $R_m$, in terms of $R_g$ and certain combinations of covariant derivatives of $m$ (with respect to ... More
Lower bounds of Lipschitz constants on foliationsJan 22 2018In this paper we consider Llarull's theorem in the foliation case and get a lower bound of the Lipschitz constant of the map $M\to S^n$ in the foliation case under the spin condition.
On Lagrangians with reduced-order Euler-Lagrange equationsJan 21 2018If a Lagrangian defining a variational problem has order $k$ then its Euler-Lagrange equations generically have order $2k$. This paper considers the case where the Euler-Lagrange equations have order strictly less than $2k$, and shows that in such a case ... More
The symplectic area of a geodesic triangle in a Hermitian symmetric space of compact typeJan 21 2018Let $M$ be an irreducible Hermitian symmetric space of compact type, and let $\omega$ be its K\"ahler form. For a triplet $(p_1,p_2,p_3)$ of points in $M$ we study conditions under which a geodesic triangle $\mathcal T(p_1,p_2,p_3)$ with vertices $p_1,p_2,p_3$ ... More
Higher genera for proper actions of Lie groupsJan 20 2018Let G be a Lie group with finitely many connected components satisfying the rapid decay (RD) property. As an example, we can take G to be a connected semisimple Lie group. Let M be a G-proper manifold with compact quotient M/G. In this paper we establish ... More
On the automorphism group of a closed G$_2$-structureJan 20 2018We study the automorphism group of a compact 7-manifold $M$ endowed with a closed non-parallel G$_2$-structure, showing that its identity component is abelian with dimension bounded by min$\{6,b_2(M)\}$. This implies the non-existence of compact homogeneous ... More
On the asymptotic behavior of static perfect fluidsJan 20 2018Static spherically symmetric solutions to the Einstein-Euler equations with prescribed central densities are known to exist, be unique and smooth for reasonable equations of state. Some criteria are also available to decide whether solutions have finite ... More
A metric deformation on fiber bundles and applicationsJan 19 2018We develop the concept of a Cheeger deformation on the context of fiber bundles with compact structure group. This procedure is used to provide metrics with positive Ricci curvature on the total space of such bundles, generalizing the results in Nash ... More
The geometry of corank $1$ surfaces in $\mathbb{R}^{4}$Jan 19 2018We study the geometry of surfaces in $\mathbb{R}^{4}$ with corank $1$ singularities. For such surfaces the singularities are isolated and at each point we define the curvature parabola in the normal space. This curve codifies all the second order information ... More
Einstein-Weyl structures on almost cosymplectic manifoldsJan 17 2018In this article, we study the Einstein-Weyl structures on almost cosymplectic manifolds. First we prove that an almost cosymplectic $(\kappa,\mu)$-manifold is Einstein or cosymplectic if it admits a closed Einstein-Weyl structure or two Einstein-Weyl ... More
Notes on Ricci solitons in $f$-cosymplectic manifoldsJan 17 2018The purpose of this article is to study an $f$-cosymplectic manifold $M$ admitting Ricci solitons. Here we consider mainly two classes of Ricci solitons on $f$-cosymplectic manifolds. One is the class of contact Ricci solitons. The other is the class ... More
Several results concerning nonexistence of proper $p$-biharmonic maps and Liouville type theoremsJan 16 2018Let $u: (M, g)\to (N, h)$ be a map between Riemannian manifolds $(M, g)$ and $(N, h)$. The $p$-bienergy of $u$ is defined by $\tau_p(u)=\int_M|\tau(u)|^pd\nu_g$, where $\tau(u)$ is the tension field of $u$ and $p>1$. Critical points of $\tau_p$ are called ... More
$L^{2}$ harmonic forms on complete special holonomy manifoldsJan 13 2018In this article,we consider $L^{2}$ harmonic forms on a complete noncompact Riemannian manifold $X$ with a parallel form $\omega$.The main result is that if $(X,\omega)$ is a complete $G_{2}$- (or $Spin(7)$-) manifold with a $d$(linear) $G_{2}$- (or $Spin(7)$-) ... More
On projective and affine equivalence of sub-Riemannian metricsJan 12 2018Consider a smooth manifold $M$ equipped with a bracket generating distribution $D$. Two sub-Riemannian metrics on $(M,D)$ are said to be projectively (resp. affinely) equivalent if they have the same geodesics up to reparameterization (resp. up to affine ... More
Asymptotic Dirichlet problems in warped productsJan 12 2018We study the asymptotic Dirichlet problem for Killing graphs with prescribed mean curvature $H$ in warped product manifolds $M\times_\varrho \mathbb{R}$. In the first part of the paper, we prove the existence of Killing graphs with prescribed boundary ... More
Asymptotics for the Ginzburg-Landau equation on manifolds with boundary under homogeneous Neumann conditionJan 11 2018On a compact manifold $M^{n}$ ($n\geq 3$) with boundary, we study the asymptotic behavior as $\epsilon$ tends to zero of solutions $u_{\epsilon}: M \to \mathbb{C}$ to the equation $\Delta u_{\epsilon} + \epsilon^{-2}(1 - |u_{\epsilon}|^{2})u_{\epsilon} ... More
Some Properties of Kenmotsu Manifolds Admitting a Semi-symmetric Non-metric ConnectionJan 09 2018The aim of this paper is to study generalized recurrent, generalized Ricci-recurrent, weakly symmetric and weakly Ricci-symmetric Kenmotsu manifolds with respect to the semi-symmetric non-metric connection.
An elliptic boundary value problem for $G_{2}$ structuresJan 05 2018We show that the $G_{2}$ holonomy equation on a manifold with boundary, with prescribed 3-form on the boundary, is elliptic. The main point is to set up a suitable linear elliptic boundary value problem. This result leads to a deformation theory. In particular ... More
Para-Sasakian manifolds and *-Ricci solitonsJan 05 2018In this paper we study a special type of metric called *-Ricci soliton on para-Sasakian manifold. We prove that if the para-Sasakian metric is a *-Ricci soliton on a manifold M, then M is either D-homothetic to an Einstein manifold, or the Ricci tensor ... More
Covariant Schrödinger semigroups on noncompact Riemannian manifoldsJan 04 2018This monograph develops the theory of covariant Schr\"odinger semigroups acting on sections of vector bundles over noncompact Riemannian manifolds from scratch. Contents: I. Sobolev spaces on vector bundles II. Smooth heat kernels on vector bundles III. ... More
Three-dimensional Ricci-degenerate Riemannian manifolds satisfying geometric equationsJan 01 2018In this paper, we study a three dimensional Ricci-degenerate Riemannian manifold $(M^3,g)$ which admits a smooth nonzero solution $f$ to the following equation: \begin{align} \label{a1a} \nabla df=\psi(f)Rc+\phi(f)g, \end{align} where $Rc$ is the Ricci ... More
Extensions of submanifold theory to non-real settings, with applicationsDec 31 2017In this thesis, we study extensions of the theory of Riemannian submanifolds in two directions. First, we will show how Riemannian geometry and submanifold theory in particular, can be generalized using the notion of 'Rinehart spaces', and it will be ... More
Constant Curvature Models in Sub-Riemannian GeometryDec 29 2017Each sub-Riemannian geometry with bracket generating distribution enjoys a background structure determined by the distribution itself. At the same time, those geometries with constant sub-Riemannian symbols determine a unique Cartan connection leading ... More
Conjectures on the Relations of Linking and Causality in Causally Simple SpacetimesDec 28 2017We formulate the generalization of the Legendrian Low conjecture of Natario and Tod (proved by Nemirovski and myself before) to the case of causally simple spacetimes. We prove a weakened version of the corresponding statement. In all known examples, ... More
Closed G$_2$-structures on non-solvable Lie groupsDec 27 2017We investigate the existence of left-invariant closed G$_2$-structures on seven-dimensional non-solvable Lie groups, providing the first examples of this type. When the Lie algebra has trivial Levi decomposition, we show that such a structure exists only ... More
Minimal elastic networksDec 27 2017We consider planar networks of three curves that meet at two junctions with prescribed equal angles, minimizing a combination of the elastic energy and the length functional. We prove existence and regularity of minimizers, and we show some properties ... More
Variational order for forced Lagrangian systemsDec 26 2017We are able to derive the equations of motion for forced mechanical systems in a purely variational setting, both in the context of Lagrangian or Hamiltonian mechanics, by duplicating the variables of the system as introduced by Galley [2013], Galley, ... More
Contact integral geometry and the Heisenberg algebraDec 26 2017Jan 03 2018Generalizing Weyl's tube formula and building on Chern's work, Alesker reinterpreted the Lipschitz-Killing curvature integrals as a family of valuations (finitely-additive measures with good analytic properties), attached canonically to any Riemannian ... More
On the flexibility of Siamese dipyramidsDec 26 2017Polyhedra called Siamese dipyramids are known to be non-flexible, however their physical models behave like physical models of flexible polyhedra. We discuss a simple mathematical method for explaining the model flexibility of the Siamese dipyramids.
Euclidean submanifolds with conformal canonical vector fieldDec 24 2017The position vector field x is the most elementary and natural geometric object on a Euclidean submanifold $M$. The position vector field plays very important roles in mathematics as well as in physics. Similarly, the tangential component x^T of the position ... More
Material groupoids and algebroidsDec 23 2017Lie groupoids and their associated algebroids arise naturally in the study of the constitutive properties of continuous media. Thus, Continuum Mechanics and Differential Geometry illuminate each other in a mutual entanglement of theory and applications. ... More
Symmetries of the space of connections on a principal G-bundle and related symplectic structuresDec 22 2017We investigate G-invariant symplectic structures on the cotangent bundle T*P of a principal G-bundle P(M,G) which are canonically related to automorphisms of the tangent bundle TP covering the identity map of P and commuting with the action of TG on TP. ... More
Lagrangian potential theory in symplectic geometryDec 10 2017The purpose of this paper is to establish a Lagrangian potential theory, analogous to the classical pluripotential theory, and to define and study a Lagrangian differential operator of Monge-Ampere type. This development is new even in ${\bf C}^n$. However, ... More
On Warped Product Gradient Yamabe SolitonNov 30 2017In this paper, we provide a necessary and sufficient conditions for the warped product $M=B\times_f F$ to be a gradient Yamabe soliton when the base is conformal to an n-dimensional pseudo-Euclidean space, which are invariant under the action of an (n-1)-dimensional ... More
Kähler metrics via Lorentzian Geometry in dimension fourNov 27 2017Given a semi-Riemannian $4$-manifold $(M,g)$ with two distinguished vector fields satisfying properties determined by their shear, twist and various Lie bracket relations, a family of K\"ahler metrics $\gK$ is constructed, defined on an open set in $M$, ... More
A Bernstein Theorem for Minimal Maps with Small Second Fundamental FormNov 27 2017We consider minimal maps $f:M\to N$ between Riemannian manifolds $(M,\mathrm{g}_M)$ and $(N,\mathrm{g}_N)$, where $M$ is compact and where the sectional curvatures satisfy $\sec_N\le \sigma\le \sec_M$ for some $\sigma>0$. Under certain assumptions on ... More
Lorentzian length spacesNov 24 2017We introduce an analogue of the theory of length spaces into the setting of Lorentzian geometry and causality theory. The r\^ole of the metric is taken over by the time separation function, in terms of which all basic notions are formulated. In this way ... More
The Local Structure of Generalized Contact BundlesNov 22 2017Generalized contact bundles are odd dimensional analogues of generalized complex manifolds. They have been introduced recently and very little is known about them. In this paper we study their local structure. Specifically, we prove a local splitting ... More
Null screen isoparametric hypersurfaces in Lorentzian space formsNov 21 2017In this paper we develop the notion of screen isoparametric hypersurface for null hypersurfaces of Robertson-Walker spacetimes. Using this formalism we derive Cartan identities for the screen principal curvatures of null screen hypersurfaces in Lorentzian ... More
Warped Product Pointwise Bi-slant Submanifolds of Kaehler ManifoldsNov 20 2017Warped product manifolds have been studied for a long period of time. In contrast, the study of warped product submanifolds from extrinsic point of view was initiated by the first author around the beginning of this century in [7, 8]. Since then the study ... More
Real hypersurfaces with $^{*}$-Ricci solitons of non-flat complex space formsNov 17 2017Kaimakamis and Panagiotidou in \cite{KP} introduced the notion of $^*$-Ricci soliton and studied the real hypersurfaces of a non-flat complex space form admitting a $^*$-Ricci soliton whose potential vector field is the structure vector field. In this ... More
Biconservative ideal hypersurfaces in Euclidean spacesNov 11 2017A biconservative submanifold of a Riemannian manifold is a sub- manifold with divergence free stress-energy tensor with respect to bienergy. These are generalizations of biharamonic submanifolds. In 2013, B. Y. Chen and M.I. Munteanu proved that $\delta(2)$-ideal ... More
On causal functionsNov 10 2017We describe, in the general setting of closed cone fields, the set of causal functions which can be approximated by smooth Lyaounov. We derive several consequences on causality theory. Dans le contexte g\'en\'eral des champs de cones ferm\'es, on d\'ecrit ... More
The Laplacian coflow on almost-abelian Lie groupsNov 10 2017We find explicit solutions of the Laplacian coflow of $G_2$-structures on seven-dimensional almost-abelian Lie groups. Moreover, we construct new examples of solitons for the Laplacian coflow which are not eingenforms of the Laplacian.
Yamabe and quasi-Yamabe solitons on Euclidean submanifoldsNov 08 2017In this paper we initiate the study of Yamabe and quasi-Yamabe solitons on Euclidean submanifolds whose soliton fields are the tangential components of their position vector fields. Several fundamental results of such solitons were proved. In particular, ... More
Low-dimensional totally geodesic submanifolds in "skew" position in the symmetric spaces of rank 2Oct 30 2017We use the Cartan representations of $SO(3)$ and $SU(3)$, and an irreducible 14-dimensional representation of $Sp(3)$ to construct certain totally geodesic submanifolds in "skew" position in the complex quadrics, the complex 2-Grassmannians and the quaternionic ... More
Contact real hypersurfaces in the complex hyperbolic quadricOct 27 2017Nov 16 2017We give a new proof of the classification of contact real hypersurfaces with constant mean curvature in the complex hyperbolic quadric ${Q^m}^* = SO_{m,2}^o/SO_mSO_2$, where $m\geq 3$. We show that a contact real hypersurface $M$ in ${Q^m}^*$ for $m\geq ... More
Invariant and anti-invariant submanifolds of special quasi-sasakian manifoldsOct 25 2017The present paper deals with the study of Chaki-pseudo parallel and Deszcz-pseudo parallel invariant submanifolds of SQ-Sasakian manifolds with respect to Levi-Civita connection and semisymmetric metric connection and obtain that these two classes are ... More
Real hypersurfaces with Miao-Tam critical metrics of complex space formsOct 18 2017Let $M$ be a real hypersurface of a complex space form with constant curvature $c$. In this paper, we study the hypersurface $M$ admitting Miao-Tam critical metric, i.e. the induced metric $g$ on $M$ satisfies the equation:$-(\Delta_g\lambda)g+\nabla^2_g\lambda-\lambda ... More
Almost conformally almost Fedosov structuresOct 16 2017We study the relations between the projective and the almost conformally symplectic structures on a smooth even dimensional manifold. We describe these relations by a single almost conformally symplectic connection with totally trace--free torsion sharing ... More
Splitting theorem for sheaves of holomorphic $k$-vectors on complex contact manifoldsOct 14 2017A complex contact structure $\gamma$ is defined by a system of holomorphic local $1$-forms satisfying the completely non-integrability condition. The contact structure induces a subbundle ${\rm Ker}\, \gamma$ of the tangent bundle and a line bundle $L$. ... More