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 (2)

• $t$-periodic light rays in conformally stationary spacetimes via Finsler geometry
• Multiplicity and stability of closed geodesics on bumpy Finsler 3-spheres