Submanifolds With Parallel Mean Curvature Vector In Locally Symmetric Space

In this thesis ,we study the n+p dimensional compact pseudo-umbilical submanifolds with parallel mean curvature in locally symmetric space. Some pinching theorems on the square of the second fundamental module length of this kind and Ricci curvature of submanifolds are obtained.The paper is organized as follows. In section 1,the historic background of the involved problem is presented and the main results are introduced. In section 2, we study the n+p dimensional compact pseudo-umbilical submanifolds with parallel mean curvature in constant curvature space, one pinching theorems on the square of the second fundamental module length of this kind are obtained. In section 3,we study the n+p dimensional compact pseudo-umbilical submanifolds with parallel mean curvature in locally symmetric space. Two pinching theorems on the square of the second fundamental module length of this kind and Ricci curvature of submanifolds are obtained.