常曲率空间中具有平行平均曲率向量的伪脐子流形

Pseudoumbilical submanifolds with parallel mean curvature vector

讨论了常曲率空间中具有平行平均曲率向量的紧致伪脐子流形成为全子流形的条件 。

Two inequlities for compact pseudoumbilical submanifolds with parallel mean curvature vector ξ(≠0) in S n+p (c) are presented, this generalizing the results which have existed, for this kind of submanifolds, two inequlities about R ii are obtained, and this submanifold M n is totally umbilical.