Translator Disclaimer
January 2021 Geodesic behavior for Finsler metrics of constant positive flag curvature on $S^2$
R. L. Bryant, P. Foulon, S. V. Ivanov, V. S. Matveev, W. Ziller
Author Affiliations +
J. Differential Geom. 117(1): 1-22 (January 2021). DOI: 10.4310/jdg/1609902015


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 metric 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 has constant flag curvature.


Download Citation

R. L. Bryant. P. Foulon. S. V. Ivanov. V. S. Matveev. W. Ziller. "Geodesic behavior for Finsler metrics of constant positive flag curvature on $S^2$." J. Differential Geom. 117 (1) 1 - 22, January 2021.


Received: 21 October 2017; Published: January 2021
First available in Project Euclid: 6 January 2021

MathSciNet: MR4195750
Digital Object Identifier: 10.4310/jdg/1609902015

Rights: Copyright © 2021 Lehigh University


This article is only available to subscribers.
It is not available for individual sale.

Vol.117 • No. 1 • January 2021
Back to Top