局部对称拟常曲率黎曼流形中伪脐子流形的Pinching定理

Pinching Theorems for Pseudo-umbilical Submanifolds in a Riemannian Manifold of Quasi-constant Curvature

讨论局部对称拟常曲率黎曼流形Nn+p中具有平行平均曲率向量的紧致伪脐子流形Mn,得到了Mn是全脐子流形的两个Pinching定理.

In this paper, we discuss the compact pseudo-umbilical submanifold M^n with parallel mean curvature in local symmetric Riemannian manifold N^n＋p of quasi-constant curvature, and obtain two Pinching theorems of M^n which is expected to be a totally umbilical submanifold.