摘要
设ＣＰｎ是具有全纯截面曲率为４的Ｆｕｂｉｎｉ－Ｓｔｕｄｙ度量的ｎ维复射影空间．设Ｍｎ是ＣＰｎ的全实子流形，若Ｍｎ关于平均曲率向量场ξ是脐性的，或Ｍｎ是极小的，则称Ｍｎ是ＣＰｎ的全实伪脐子流形．本文得到关于ＣＰｎ的紧致全实伪脐子流形Ｍｎ的Ｓ，ξ和Ｈ这三个重要不变量的几个命题和定理．
Let CP n be an n-dimensional complex projective space with Fubini-Study metric of constant holomorphic sectional curvature 4 and M n be a totally real submanifold in CP n. If M n is either umbilical in respect to mean curvature vector field ξ or minimal, then M n is called a totally real pseudo-umbilical submanifold in CP n. In this paper, we get several propositions and theorems about S, ξ and H which are three important invariants in compact totally real pseudo-umbilical submanifold M n.
出处
《杭州大学学报（自然科学版）》
CSCD
1998年第2期8-14,共7页
Journal of Hangzhou University Natural Science Edition
基金
杭州大学学生科研基金
关键词
复射影空间
伪脐
全实子流形
complex projective space
pseudo-umbilical
totally real submanifold
