Finsler Metrics and Closed Geodesics

一方面讨论了Finsler度量的曲率性质与最短闭测地线的长度之间的关系;内射性半径和另一方面，存在性结果的封闭测地线的紧流形携带Finsler度量将被考虑。在更详细的以下问题将被调查：1。申请人对正旗曲率的不可逆芬斯勒度量的最短闭测地线给出的长度估计的相等性是否意味着旗曲率是常数？2.有可能改进申请人提出的具有正旗曲率的紧致和单连通黎曼流形的内射性半径的估计的下界吗？是否存在一个不依赖于可逆性的下限？3.在紧致秩一对称空间上，讨论了具有不可逆Finsler度量的两条闭测地线的存在性。

On one hand the connection between curvature properties of Finsler metrics and the length of the shortest closed geodesic resp. the injectivity radius and on the other hand existence results for closed geodesics on compact manifolds carrying a Finsler metric will be considered. In more detail the following problems will be investigated:1. Does equality in the length estimate given by the applicant for the shortest closed geodesic of a non-reversible Finsler metric of positive flag curvature imply that the flag curvature is constant?2. Is is possible to improve the lower bound in the estimate presented by the applicant for the injectivity radius of a compact and simply-connected Riemannian manifold with positive flag curvature? Is there a lower bound which does not depend on the reversibility?3. The existence of two closed geodesics on a compact rank one symmetric space witha bumpy non-reversible Finsler metric.