关于局部对称空间的几个Pinching定理  

Several Pinching Theorems on Locally Symmetric Space

作　　者：朱华 陈梦 ZHU Hua;CHEN Meng(School of Mathematics and Computer Science,Panzhihua University,Panzhihua Sichuan 617000,China;School of Basic Medical Science,North Sichuan Medical College,Nanchong Sichuan 637100,China)

机构地区：[1]攀枝花学院数学与计算机学院,四川攀枝花617000 [2]川北医学院基础医学院,四川南充637100

出　　处：《西南师范大学学报（自然科学版）》2018年第10期31-34,共4页Journal of Southwest China Normal University(Natural Science Edition)

基　　金：国家自然科学基金项目(11471188)

摘　　要：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.

关 键 词：局部对称空间 平行平均曲率向量 伪脐子流形 

分 类 号：O186.1[理学—数学]