We prove that a Finsler manifold Fm is of constant curvature K = 1 if and only if the unit horizontal Liouville vector field is a Killing vector field on the indicatrix bundle IM of Fm.

We review the current status of Finsler–Lagrange geometry and generalizations. The goal is to aid non–experts on Finsler spaces, but physicists and geometers skilled in general relativity and particle theories, to understand the crucial importance of such geometric methods for applications in modern physics. We also would like to orient mathematicians working in generalized Finsler and Kähler g...

We determine a 2-codimensional para-CR structure on the slit tangent bundle T0M of a Finsler manifold (M,F ) by imposing a condition regarding the almost paracomplex structure P associated to F when restricted to the structural distribution of a framed para-f -structure. This condition is satisfied when (M,F ) is of scalar flag curvature (particularly constant) or if the Riemannian manifold (M,...

We present an approach for detecting multiword phrases in mathematical text corpora. The method used is based on characteristic features of mathematical terminology. It makes use of a software tool named Lingo which allows to identify words by means of previously defined dictionaries for specific word classes as adjectives, personal names or nouns. The detection of multiword groups is done algo...

The flag curvature is a natural extension of the sectional curvature in Riemannian geometry, and the S-curvature is a non-Riemannian quantity which vanishes for Riemannian metrics. There are (incomplete) nonRiemannian Finsler metrics on an open subset in Rn with negative flag curvature and constant S-curvature. In this paper, we are going to show a global rigidity theorem that every Finsler met...

It is shown that, on a manifold with a Finsler metric of Lorentzian signature, the lightlike geodesics satisfy the following variational principle. Among all lightlike curves from a point q (emission event) to a timelike curve γ (worldline of receiver), the lightlike geodesics make the arrival time stationary. Here “arrival time” refers to a parametrization of the timelike curve γ. This variati...

Lagrange geometry is the geometry of the tensor field defined by the fiberwise Hessian of a nondegenerate Lagrangian function on the total space of a tangent bundle. Finsler geometry is the geometrically most interesting case of Lagrange geometry. In this paper, we study a generalization which consists of replacing the tangent bundle by a general tangent manifold, and the Lagrangian by a family...

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),...