# Geodesic behavior for Finsler metrics of constant positive flag curvature on S^2

Accepted

Journal Article

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 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 constant positive flag curvature is completely integrable. Finally, we give an example of a Finsler metric on S^2 with positive flag curvature such that no two closed geodesics intersect and show that this is not possible when the metric is reversible or have constant flag curvature

### Full Text

### Duke Authors

### Cited Authors

- Bryant, R; Foulon, P; Ivanov, S; Matveev, VS; Ziller, W

### Published In

- Journal of Differential Geometry