An algebraic characterisation for Finsler metrics of constant flag curvature

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...

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...

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...

Two-Dimensional Finsler Metrics with Constant Curvature

We construct infinitely many two-dimensional Finsler metrics on S 2 and D 2 with non-zero constant flag curvature. They are all not locally projectively flat.