论文标题
同源循环类别的临界值的上限
Upper bounds for the critical values of homology classes of loops
论文作者
论文摘要
在此简短的说明中，我们讨论了同源类别的临界值的上限，在带有riemannian或Finsler阳性RICCI曲率的歧管的基于和自由的循环空间中。特别是，因此，在简单连接的$ n $ dimensional corlold curvature $ \ textrm {ric} \ ge n-1 $上具有长度$ \ lenπ$。
In this short note we discuss upper bounds for the critical values of homology classes in the based and free loop space of manifolds carrying a Riemannian or Finsler metric of positive Ricci curvature. In particular it follows that a shortest closed geodesic on a simply-connected $n$-dimensional manifold of positive Ricci curvature $\textrm{Ric} \ge n-1$ has length $\le n π.$
