关于局部对称空间中的伪脐子流形

On the Pseudo-umbilical Submanifolds of a Locally Symmetric Space

中文关键词:  局部对称  全脐子流形  平行平均曲率向量场

英文关键词:locally symmetric  pseudo-umbiIical submanifolds  totally umbilical

中文摘要:

      本文讨论了局部对称完备黎曼流形中的紧致伪脐子流形，且具有平行平均山率向量场。得到了这类子流形成为全脐子流形及其余维数减小的几个拼挤定理。

英文摘要:

      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.