Given the class of Finsler spaces with Lorentzian signature [Formula: see text] on a manifold endowed timelike vector field satisfying at any point slit tangent bundle, pseudo-Riemannian metric defined is associated to fundamental tensor text]. Furthermore, an affine, torsion free connection Chern determined by The definition average does not make use Therefore, there no direct relation between...

We study homogeneous Lorentzian manifolds M=G/L of a connected reductive Lie group G modulo subgroup L, under the assumption that M is (almost) G-effective and isotropy representation totally reducible. show description such reduces to case semisimple groups G. Moreover, we prove space reductive. describe all reducible subgroups Lorentz divide them into three types. The Type I are compact, whil...

In a general-relativistic spacetime (Lorentzian manifold), gravitational lensing can be characterized by a lens map, in analogy to the lens map of the quasi-Newtonian approximation formalism. The lens map is defined on the celestial sphere of the observer (or on part of it) and it takes values in a two-dimensional manifold representing a two-parameter family of worldlines. In this article we us...

In this paper we consider the images taken from pairs of parabolic catadioptric cameras separated by discrete motions. Despite the nonlinearity of the projection model, the epipolar geometry arising from such a system, like the perspective case, can be encoded in a bilinear form, the catadioptric fundamental matrix. We show that all such matrices have equal Lorentzian singular values, and they ...

One of the known mathematical descriptions of singularities in General Relativity is the b-boundary, which is a way of attaching endpoints to inextendible endless curves in a spacetime. The b-boundary of a manifold M with connection Γ is constructed by forming the Cauchy completion of the frame bundle LM equipped with a certain Riemannian metric, the b-metric G. We study the geometry of (LM, G)...

Fermion fields on an M-theory five-brane carry a representation of the double cover of the structure group of the normal bundle. It is shown that, on an arbitrary oriented Lorentzian six-manifold, there is always an Sp 2 twist that allows such spinors to be defined globally. The vanishing of the arising potential obstructions does not depend on spin structure in the bulk, nor does the six-manif...

Motivated by many applications (geophysical flows, general relativity), we attempt to set the foundations for a study of entropy solutions to nonlinear hyperbolic conservation laws posed on a (Riemannian or Lorentzian) manifold. The flux of the conservation laws is viewed as a vector-field on the manifold and depends on the unknown function as a parameter. We introduce notions of entropy soluti...

The Cauchy problem for harmonic maps from Minkowski space with its standard flat metric to a certain non-constant curvature Lorentzian 2-metric is studied. The target manifold is distinguished by the fact that the Euler–Lagrange equation for the energy functional is Darboux integrable. The time evolution of the Cauchy data is reduced to an ordinary differential equation of Lie type associated t...

In this paper, we introduce a Lorentzian Anosov family (LAfamily) up to sequence of distributions null vectors. We prove for each p Mi, where Mi is manifold i Z the tangent space at has unique splitting and varies continuously on via distance function created by torsion-free semi-Riemannian connection. present three examples LA-families. Also, define shadowing property type I II some results re...