Let Ω be a domain in a smooth complete Finsler manifold, and let G be the largest open subset of Ω such that for every x in G there is a unique closest point from ∂Ω to x (measured in the Finsler metric). We prove that the distance function from ∂Ω is in C k,α loc (G ∪ ∂Ω), k ≥ 2 and 0 < α ≤ 1, if ∂Ω is in C k,α .

In this paper we first study some global properties of the energy functional on a nonreversible Finsler manifold. In particular we present a fully detailed proof of the Palais–Smale condition under the completeness of the Finsler metric. Moreover we define a Finsler metric of Randers type, which we call Fermat metric, associated to a conformally standard stationary spacetime. We shall study the...

In this paper we prove some results on the number of geodesics connecting two points or two submanifolds on a non-reversible complete Finsler manifold, in particular for complete Randers metrics. We apply the abstract results to the study of light rays and timelike geodesics with fixed energy on a standard stationary Lorentzian manifold.

A Finsler metric is of sectional flag curvature if its flag curvature depends only on the section. In this article, we characterize Randers metrics of sectional flag curvature. It is proved that any non-Riemannian Randers metric of sectional flag curvature must have constant flag curvature if the dimension is greater than two. 0. Introduction Finsler geometry has a long history dated from B. Ri...

Given the Finsler structure (M, F) on a manifold M, a Riemannian structure (M, h) and a linear connection on M are defined. They are obtained as the " average " of the Finsler structure and the Chern connection. This linear connection is the Levi-Civita connection of the Riemannian metric h. The relation between parallel transport of the Chern connection and the Levi-Civita connection of h are ...

We define the Liouville distribution on the tangent bundle of a pseudo-Finsler manifold and prove that it is integrable. Also, we find geometric properties of both leaves of Liouville distribution and the vertical distribution.

In this paper we continue the study of the complex Beil metrics, in complex Finsler geometry, [18]. Primarily, we determine the main geometric objects corresponding to these metrics, e.g. the Chern-Finsler complex non-linear connection, the Chern-Finsler complex linear connection and the holomorphic curvature. We focus our study on the cases when a complex Finsler space, endowed with a complex ...

Based on the analogue spacetime programme, and many other ideas currently mooted in “quantum gravity”, there is considerable ongoing speculation that the usual pseudoRiemannian (Lorentzian) manifolds of general relativity might eventually be modified at short distances. Two specific modifications that are often advocated are the adoption of Finsler geometries (or more specifically, pseudo-Finsl...