Generic Existence of Infinitely Many Non-contractible Closed Geodesics on Compact Space Forms  

作　　者：Hui Liu Yu Chen Wang 

机构地区：[1]School of Mathematics and Statistics,Wuhan University,Wuhan,430072,P.R.China [2]School of Mathematics,Tianjin Normal University,Tianjin,300384,P.R.China

出　　处：《Acta Mathematica Sinica,English Series》2024年第7期1674-1684,共11页数学学报（英文版）

基　　金：supported by NSFC(Grant Nos.12371195,12022111);the Fundamental Research Funds for the Central Universities(Grant No.2042023kf0207);the second author was partially supported by NSFC(Grant No.11831009);Fundings of Innovating Activities in Science and Technology of Hubei Province。

摘　　要：Let M=S^(n)/Γand h be a nontrivial element of finite order p inπ_(1)(Μ),where the integers n,p≥2,Γis a finite abelian group which acts freely and isometrically on the n-sphere and therefore M is diffeomorphic to a compact space form.In this paper,we prove that there are infinitely many non-contractible closed geodesics of class[h]on the compact space form with C^(r)-generic Finsler metrics,where 4≤r≤∞.The conclusion also holds for Cr-generic Riemannian metrics for 2≤r≤∞.The proof is based on the resonance identity of non-contractible closed geodesics on compact space forms.

关 键 词：Compact space forms non-contractible closed geodesics generic Finsler metrics resonance identity 

分 类 号：O186.1[理学—数学]