Mathematics > Differential Geometry
[Submitted on 20 Apr 2018]
Title:Two closed geodesics on compact bumpy Finsler manifolds
View PDFAbstract:In this paper, we prove there are at least two closed geodesics on any compact bumpy Finsler $n$-manifold with $n\ge 2$. Thus generically there are at least two closed geodesics on compact Finsler manifolds. Furthermore, there are at least two closed geodesics on any compact Finsler $2$-manifold, and this lower bound is achieved by the Katok 2-sphere, cf. \cite{Kat}.
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