Related papers: $A^\nabla$-tensors on lightlike hypersurfaces
We explore the class of triples (M, nabla, P) where M is a manifold, nabla is an affine connection in M and P is a G-structure in M. Inside this class there are infinitesimally homogeneous manifolds, characterized by having G-constant…
In this paper, we first investigate several rigidity problems for hypersurfaces in the warped product manifolds with constant linear combinations of higher order mean curvatures as well as "weighted'' mean curvatures, which extend the work…
In this paper we look at the question of integrability, or not, of the two natural almost complex structures $J^{\pm}_\nabla$ defined on the twistor space $J(M,g)$ of an even-dimensional manifold $M$ with additional structures $g$ and…
The class of the Riemannian almost product manifolds with nonintegrable structure is considered. Some identities for curvature tensor as certain invariant tensors and quantities are obtained.
We study locally homogeneous rigid geometric structures on surfaces. We show that a locally homogeneous projective connection on a compact surface is flat. We also show that a locally homogeneous unimodular affine connection on a two…
We prove existence and uniqueness of entire spacelike hypersurfaces in the Minkowski space with prescribed negative scalar curvature, and with given values at infinity which stay at a bounded distance of a lightcone.
Given a compact Riemannian manifold $M$, we consider a warped product $\bar M = I \times_h M$ where $I$ is an open interval in $\Bbb R$. For a positive function $\psi$ defined on $\bar M$, we generalized the arguments in \cite{GRW2015} and…
The condition for the curvature of a statistical manifold to admit a kind of standard hypersurface is given. We study the statistical hypersurfces of some types of the statistical manifolds $(M, \nabla, g )$, which enable $(M,…
In this paper, we show that ``$L$-complete null hypersurfaces'' (i.e. ruled hypersurfaces foliated by entirety of light-like lines) as wave fronts in the $(n+1)$-dimensional Lorentz-Minkowski space are canonically induced by hypersurfaces…
We find a necessary and sufficient condition for the existence of the tensor product of modules over a Lie conformal algebra. We provide two algebraic constructions of the tensor product. We show the relation between tensor product and…
The geometry and topology of complete nonorientable maximal surfaces with lightlike singularities in the Lorentz-Minkowski 3-space are studied. Some topological congruence formulae for surfaces of this kind are obtained. As a consequence,…
Symmetric hyperbolic systems of equations are explicitly constructed for a general class of tensor fields by considering their structure as r-fold forms. The hyperbolizations depend on 2r-1 arbitrary timelike vectors. The importance of the…
We use curvature decompositions to construct generating sets for the space of algebraic curvature tensors and for the space of tensors with the same symmetries as those of a torsion free, Ricci symmetric connection; the latter naturally…
A $(TE)$-structure $\nabla$ over a complex manifold $M$ is a meromorphic connection defined on a holomorphic vector bundle over $\mathbb{C}\times M$, with poles of Poincar\'e rank one along $\{ 0 \} \times M.$ Under a mild additional…
We study singular hypersurfaces in tensor multi-scalar theories of gravity. We derive in a distributional and then in an intrinsic way, the general equations of junction valid for all types of hypersurfaces, in particular for lightlike…
Let $X$ be a smooth projective variety of dimension $n\geq 3$, and let $L$ be an ample line bundle on $X$. In this article, we study the algebraic hyperbolicity of a very general section of the adjoint linear series $|K_X+mL|$ when the…
Using the Blaschke-Berwald metric and the affine shape operator of a hypersurface M in the (n+1)-dimensional real affine space we can define some generalized curvature tensor named the Opozda-Verstraelen affine curvature tensor. In this…
The Standard Model does not explain the hierarchy problem. Before the discovery of nonzero lepton mixing angle {\theta}13 high hopes in explanation of the shape of the lepton mixing matrix were combined with non abelian symmetries.…
Metal nanowires and nanoparticles that facilitate surface plasmons are of contemporary interest in nanophotonics, thermoplasmonics and optoelectronics. They facilitate not only subwavelength light propagation and localization capabilities,…
Anti-de Sitter space is the Lorentzian space form with negative curvature. In this paper we consider lightlike hypersurfaces along spacelike submanifolds in anti-de Sitter space with general codimension. In particular, we investigate the…