关于球的紧致子流形的几个pinching定理

SOME PINCHING THEOREMS ON COMPACT SUBMANIFOLDS OF SPHERE

本文讨论球的紧致子流形，研究具平行平均曲率向量的，具平坦法丛的、以及伪脐子流形成为全脐子流形的条件，得到几个关于第二基本形式长度千方Ｓ的ｐｉｎｃｈｉｎｇ条件。

This pepediscusses compact submanifoldsoftheunit sphere Study is made on conditions ofsubmanifolds with parallel mean curvature vector,submanifolds with flat normal bundle andpseudo-umbilical submanifolds to be umbilical respectively。 Several pinching conditions are obtained about the square of length of the second fundamental form。