We apply topological methods and a Lusternik-Schnirelmann-type approach to prove existence results for closed geodesics of Finsler metrics on spheres and projective spaces. The main tool in the proofs are spherical complexities, which have been introduced in earlier work of the author. Using them, we show how pinching conditions and inequalities between a Finsler metric and a globally symmetric metric yield the existence of multiple closed geodesics as well as upper bounds on their lengths.

中文翻译：

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封闭的Finsler测地线通过球面复杂度的存在​​结果

我们使用拓扑方法和Lusternik-Schnirelmann型方法来证明球体和投影空间上Finsler度量的封闭测地线的存在结果。证明中的主要工具是球形复杂度，这在作者的早期工作中已经介绍过。使用它们，我们展示了Finsler度量和全局对称度量之间的捏合条件和不等式如何导致存在多个闭合测地线以及它们长度的上限。