Existence of closed geodesics on positively curved Finsler manifolds

TL;DR

This paper investigates the existence, quantity, length, and stability of closed geodesics on spheres and projective spaces equipped with positively curved, non-reversible Finsler metrics.

Contribution

It provides new results on the number, length, and stability of closed geodesics specifically for non-reversible Finsler metrics with positive flag curvature.

Findings

Results on the number of closed geodesics

Bounds on the length of closed geodesics

Analysis of stability properties

Abstract

For non-reversible Finsler metrics of positive flag curvature on spheres and projective spaces we present results about the number and the length of closed geodesics and about their stability properties.