The second closed geodesic, the fundamental group, and generic Finsler metrics

TL;DR

This paper establishes conditions under which compact manifolds with infinite fundamental groups possess at least two distinct closed geodesics, extending results from Riemannian to Finsler metrics.

Contribution

It provides new topological and metric criteria for the existence of multiple closed geodesics on manifolds, bridging Riemannian and Finsler geometry.

Findings

Existence of two geometrically distinct closed geodesics under certain conditions

Extension of generic Riemannian results to Finsler metrics

Conditions related to fundamental group influence geodesic multiplicity

Abstract

For compact manifolds with infinite fundamental group we present sufficient topological or metric conditions ensuring the existence of two geometrically distinct closed geodesics. We also show how results about generic Riemannian metrics can be carried over to Finsler metrics.