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 ...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.展开更多
Let(RP^(n),F)be a bumpy and irreversible Finsler n-dimensional real projective space with reversibilityλand flag curvature K satisfying(λ/1+λ)^(2)<K≤1 when n is odd,and K≥0 when n is even.We show that if there...Let(RP^(n),F)be a bumpy and irreversible Finsler n-dimensional real projective space with reversibilityλand flag curvature K satisfying(λ/1+λ)^(2)<K≤1 when n is odd,and K≥0 when n is even.We show that if there exist exactly 2[n+1/2]prime closed geodesics on such(RP^(n),F),then all of them are non-contractible,which coincides with the Katok’s examples.展开更多
基金supported by NSFC(Grant Nos.12371195,12022111)the Fundamental Research Funds for the Central Universities(Grant No.2042023kf0207)+1 种基金the second author was partially supported by NSFC(Grant No.11831009)Fundings of Innovating Activities in Science and Technology of Hubei Province。
文摘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.
基金The first author was partially supported by National Key R&D Program of China(Grant No.2020YFA0713300)NSFC(Grant Nos.11671215 and 11790271)+1 种基金LPMC of MOE of China and Nankai Universitythe second author was partially supported by NSFC(Grant Nos.11771341 and 12022111)。
文摘Let(RP^(n),F)be a bumpy and irreversible Finsler n-dimensional real projective space with reversibilityλand flag curvature K satisfying(λ/1+λ)^(2)<K≤1 when n is odd,and K≥0 when n is even.We show that if there exist exactly 2[n+1/2]prime closed geodesics on such(RP^(n),F),then all of them are non-contractible,which coincides with the Katok’s examples.
