摘要
本文讨论复射影空间 CP^n 中的全实子流形 M 在什么条件下为全测地或全脐的问题,就具有平行中曲率向量的这种子流形,文中给出利用 M 的数量曲率满足不等式来判断的一些定理(见定理1—4)。
In this paper,we establish the following theorems:Theorem 1 Let M be totally real comfact submanifolds with parallelmean curvature vector in CP^n.If scalar curvature of M satisfies:r≥n(n-1)+n^2H^2-(1+n)/(1+√n)then M is totally umbilical.Theorem 2 Let M be totally real comfact submanifolds with parallelmean curvature vector in CP^n,If scalar curvature of M satisfies:r>((n-2)n^2)/(n-1)H^2+(n-2)(n+1)then M is totally geodesic.
出处
《数学杂志》
CSCD
北大核心
1992年第4期383-390,共8页
Journal of Mathematics
