The optimal lower bound estimation of the number of closed geodesics on Finsler compact space form $S^{2n+1}/Gamma$
The optimal lower bound estimation of the number of closed geodesics on Finsler compact space form $S^{2n+1}/Gamma$
复制标题
Finsler紧空间上闭合测地线数量的最优下界估计形式$S^{2n 1}/Gamma$
DOI：
10.1007/s00526-019-1567-3
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发表时间：
2019
影响因子：
2.1
通讯作者：
Liu Hui
中科院分区：
文献类型：
--
作者：
Liu Hui
Let,is a finite group which acts freely and isometrically on the-sphere and thereforeMis diffeomorphic to a compact space form. In this paper, we first investigate Katok’s famous example about irreversible Finsler metrics on the spheres to study the topological structure of the contractible component of the free loop space on the compact space formM, then we apply the result to establish the resonance identity for homologically visible contractible minimal closed geodesics on every Finsler compact space form (M,F) when there exist only finitely many distinct contractible minimal closed geodesics on (M,F). As its applications, using this identity and the enhanced common index jump theorem for symplectic paths proved by Duan et al. (Calc Var PDEs 55(6):55–145, 2016), we show that there exist at leastdistinct closed geodesics on every compact space formwith a bumpy irreversible Finsler metricFunder some natural curvature condition, which is the optimal lower bound due to Katok’s example.
