论文标题
阳性RICCI曲率和最短周期性测量长度的长度
Positive Ricci Curvature and the Length of a shortest periodic geodesic
论文作者
论文摘要
令$ m^n $为dimension $ n \ geq 2 $的封闭式riemannian流形，带有ricci曲率$ ric \ geq n-1 $。我们将证明，在$ m^n $上的封闭环的空间中，尺寸$ m $的任何范围都是同型在长度的闭环空间中，最多为$8πm$。因此，$ m^n $上最短的周期性测量长度的长度从上面的$8π（n-1）$限制。
Let $M^n$ be a closed Riemannian manifold of dimension $n\geq 2$, with Ricci curvature $Ric \geq n-1$. We will show that any sphere of dimension $m$ in the space of closed loops on $M^n$ is homotopic to the sphere in the space of closed loops of length at most $8 πm$. It follows that the length of a shortest periodic geodesic on $M^n$ is bounded from above by $8 π(n-1)$.
