In this paper we prove several multiplicity results of t-periodic light rays in conformally stationary spacetimes using the Fermat metric and the extensions of the classical theorems of Gromoll-Meyer and Bangert-Hingston to Finsler manifolds. Moreover, we exhibit some stationary spacetimes with a finite number of t-periodic light rays and compute a lower bound for the period of the light rays w...

The flag curvature of the Numata Finsler structures is shown to admit a nontrivial prolongation to the one-dimensional case, revealing an unexpected link with the Schwarzian derivative of the diffeomorphisms associated with these Finsler structures. Mathematics Subject Classification 2000: 58B20, 53A55 1 Finsler structures in a nutshell 1.1 Finsler metrics A Finsler structure is a pair (M,F ) w...

tournaments are a type of directed graph which have been used to study the geometry classical flag manifolds. We became interested in this graphs because combinatorial properties can be geometric [21]introduced Forman-Ricci curvature for and undirected hypergraphs obtained as particular case. In work we present basic ideas about Forman- Ricci graphs, characterize parabolic terms calculate any t...

We study non-reversible Finsler metrics with constant flag curvature 1 on S^2 and show that the geodesic flow of every such metric is conjugate to one Katok's examples, which form a 1-parameter family. In particular, length shortest closed complete invariant flow. also show, in any dimension, positive completely integrable. Finally, we give an example on~$S^2$ no two geodesics intersect this no...

The translative intersection formula of integral geometry yields an expression for the mean Euler characteristic a stationary random closed set intersected with fixed observation window. We formulate this result in setting sets positive reach and using flag measures which yield curvature as marginals. As application, we consider excursion fields $C^{1,1}$ realizations, particular, Gaussian fiel...