On Projectively Flat Finsler Warped Product Metrics of Constant Flag Curvature

Projectively Flat Finsler Metrics of Constant Curvature

It is the Hilbert’s Fourth Problem to characterize the (not-necessarilyreversible) distance functions on a bounded convex domain in R such that straight lines are shortest paths. Distance functions induced by a Finsler metric are regarded as smooth ones. Finsler metrics with straight geodesics said to be projective. It is known that the flag curvature of any projective Finsler metric is a scala...

On a class of locally projectively flat Finsler metrics

‎In this paper we study Finsler metrics with orthogonal invariance‎. ‎We‎ ‎find a partial differential equation equivalent to these metrics being locally projectively flat‎. ‎Some applications are given‎. ‎In particular‎, ‎we give an explicit construction of a new locally projectively flat Finsler metric of vanishing flag curvature which differs from the Finsler metric given by Berwald in 1929.

Nonreversible Finsler Metrics of Positive Flag Curvature

Finsler Manifolds with Nonpositive Flag Curvature and Constant S-curvature

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...

Geodesic behavior for Finsler metrics of constant positive flag curvature on S

We study non-reversible Finsler metrics with constant flag curvature 1 on S and show that the geodesic flow of every such metric is conjugate to that of one of Katok’s examples, which form a 1-parameter family. In particular, the length of the shortest closed geodesic is a complete invariant of the geodesic flow. We also show, in any dimension, that the geodesic flow of a Finsler metrics with c...