On the Pseudo-umbilical Submanifolds of a Locally Symmetric Space

Abstract:

      In this paper, We discussed the compact pseudo-umbilical submanifolds Mⁿ with parallel mean curvature vector in a locally symmetric Riemannian manifold N^n+p, and get some pinching theorems that Mⁿ be an totally umbilical submanifold and reduction of the codimension.