摘要
本文证明了:设M^n是复射影空间 CP^n 的紧致全实 n 维极小子流形,如果M^n 的第二基本形式长度的平方 S≤(n+1)/(1+((n-1)/2n)^(1/2)),则 M^n 是全测地的或 n=2,M^2=S^1×S^2。
The following theorem is obtained. Let Mn bean n-dimensional compact totally real minimal submanifold immersed in a complex protective space CPn. IfS≤(n+1)/(1+ (n-1)/2n ), then Mn is either totally geodesic or n = 2, M2=S1 ×S1,where S denotes the square of the length of the second fundamental form of Mn.
关键词
复射影空间
全实子流形
全测地
complex projective space, totally real submanifold, totally geodesic.
