Resonance identity and multiplicity of non-contractible closed geodesics on Finsler RPn
Resonance identity and multiplicity of non-contractible closed geodesics on Finsler RPn
复制标题
Finsler RPn 上不可收缩闭合测地线的共振恒等式和重数
DOI：
10.1016/j.aim.2017.07.024
复制
发表时间：
2017
影响因子：
1.7
通讯作者：
Yuming Xiao
中科院分区：
文献类型：
--
作者：
Hui Liu;Yuming Xiao
本文首先建立了Finsler n维真实的射影空间（RPn，F）上同调可见的非收缩素闭测地线的共振恒等式，当（RPn，F）上仅存在n个不同的非收缩闭测地线时，其中n≥ 2.然后作为这个共振恒等式的一个应用，我们证明了R Pn上至少存在两个不同的非可缩闭测地线，它们具有凹凸不平的不可逆Finsler度量.结合文献[14]和[39]中关于凹凸和可逆Finsler度量的两个结果，得到了每个具有凹凸Finsler度量的R Pn至少有两条不同的不可收缩闭测地线.
In this paper, we establish first the resonance identity for non-contractible homologically visible prime closed geodesics on Finsler n-dimensional real projective space (R P n, F) when there exist only finitely many distinct non-contractible closed geodesics on (R P n, F), where the integer n≥ 2. Then as an application of this resonance identity, we prove the existence of at least two distinct non-contractible closed geodesics on R P n with a bumpy and irreversible Finsler metric. Together with two previous results on bumpy and reversible Finsler metrics in [14] and [39], it yields that every R P n with a bumpy Finsler metric possesses at least two distinct non-contractible closed geodesics.