Multiple closed geodesics on bumpy Finsler $n$-spheres

Abstract

In this paper we prove that for every bumpy Finsler metric $F$ on every rationally homological $n$-dimensional sphere $S^n$ with $n\ge 2$, there exist always at least two distinct prime closed geodesics.

22 pages

References in corpus (1)

• Geodesics in Randers spaces of constant curvature

Cited by in corpus (13)

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• Topological structure of non-contractible loop space and closed geodesics on real projective spaces with odd dimensions
• Closed geodesics on positively curved spheres $S^n$ with Finsler metric induced by $(\mathbb{R}{P}^n,F)$