关于局部对称空间的几个Pinching定理

Several Pinching Theorems on Locally Symmetric Space

研究了局部对称空间中具有平行平均曲率向量的紧致伪脐子流形,利用活动标架法和Hopf极大值原理讨论了子流形的Pinching问题,即估算子流形第二基本形式模长的平方的Laplacian,再对截面曲率和Ricci曲率加以某种限制,得到这类子流形成为全脐子流形的几个拼挤定理.

This paper is mainly to discuss the compact pseudo-umbilical submanifold with parallel mean curvature vector in the locally symmetric space,by means of the active frame method and the Hopf maximum principle.We have studied the Pinching problem of submanifold that we get some rigidity theorems by estimating the Laplacian of the square of the length of the second fundamental form and giving some restrictions to the sectional curvature and the Ricci curvature,and we get some pinching theorems that M n can become a totally umbilical submanifold.