局部对称空间中具有平行中曲率向量的伪脐子流形

Pseudo-Umbilical Submanifolds with Parallel Mean Curvature Vector in Locally Symmetric Space

设Nn+p是截面曲率KN满足1/2<δ<KN<1的n+p维局部对称完备的δ-Pinching黎曼流形。Mn是Nn+p的紧致伪脐子流形。本文讨论了这类子流形关于第二基本形式模长的平方、截面曲率及Ricci曲率有关的Pinching定理。

Letbe a n ＋p-dimensional locally symmetric complete Riemannian manifold with sectional curvaturesatisfiesand be an n-dimensinal compact Pseudo-Umbilical submanifold in .In this paper, we discussed the Pinching theorem about this manifolds with, Rijij curvature and Ricci curvature.