We obtain some results in both, Lorentz and Finsler geometries, by using a correspondence between the conformal structure of standard stationary spacetimes on M = R × S and Randers metrics on S. In particular: (1) For stationary spacetimes: we give a simple characterization on when R×S is causally continuous or globally hyperbolic (including in the latter case, when S is a Cauchy hypersurface),...

In this essentially selfcontained paper first we establish an intrinsic version and present a coordinate-free deduction of the so-called Rapcsák equations, which provide, in the form of 2nd order PDE-s, necessary and sufficient conditions for a Finsler structure to be projectively related to a spray. From another viewpoint, the Rapcsák equations are the conditions for the Finsler-metrizability ...

in this paper the general relatively isotropic l -curvature finsler metrics are studied. it isshown that on constant relatively landsberg spaces, the concepts of weakly landsbergian, landsbergianand generalized landsbergian metrics are equivalent. some necessary conditions for a relativelyisotropic l -curvature finsler metric to be a riemannian metric are also found.

For the general class of pseudo-Finsler spaces with (α,β)-metrics, we establish necessary and sufficient conditions such that these admit a Finsler spacetime structure. This means fundamental tensor has Lorentzian signature on conic subbundle tangent bundle thus existence cone future-pointing time-like vectors is ensured. The identified (α,β)-Finsler spacetimes are candidates for applications i...

The object of this talk is to illustrate the usefulness of symplectic geometry in understanding new features of geometrical optics for spinning light in refractive media, e.g., the subtle transverse shift of light beams across an interface, which has been coined the Spin Hall Effect of Light [1]. We reformulate Fermat’s principle to describe spinning light rays in Riemannian three-manifolds, (M...

The main purpose of this article is to introduce a comprehensive, unified theory of the geometry of all connections. We show that one can study a connection via a certain, closely associated second-order differential equation. One of the most important results is our extended Ambrose-Palais-Singer correspondence. We extend the theory of geodesic sprays to certain second-order differential equat...

The kinetic theory is formulated with respect to anholonomic frames of reference on curved spacetimes. By using the concept of nonlinear connection we develop an approach to modelling locally anisotropic kinetic processes and, in corresponding limits, the relativistic non–equilibrium thermodynamics with local anisotropy. This lead to a unified formulation of the kinetic equations on (pseudo) Ri...

Considering a complex Lagrange space ([24]), in this paper the electromagnetic tensor fields are defined as sum between differential of Liouville 1-form and symplectic 2-form relative to adapted frames Chern–Lagrange nonlinear connection. In particular, an electrodynamics theory on Finsler is obtained. We show that our definition tensors has physical meaning these generate adequate field which ...

We introduce the submersion between two spray structures and propose technique in geometry. Using this technique, as well global invariant frames on a Lie group, we setup general theoretical framework for homogeneous define vector field $$\eta $$ connection operator N manifold $$(G/H,{\mathbf {G}})$$ with linear decomposition $${\mathfrak {g}}={\mathfrak {h}}+{\mathfrak {m}}$$ . These notions g...