局部对称空间中关于第二基本形式模长平方的一个刚性定理

A rigid theorem about second fundamental form modula length square in the local symmetrical space

设Nn+p是截面曲率KN满足1/2<δ≤KN≤1的n+p维局部对称完备黎曼流形,Mn是Nn+p的具有平行平均曲率向量的n维紧致子流形,我们讨论这类子流形,得到其关于第二基本形式模长的平方、及余维数减小的刚性定理,将常曲率空间中的类似问题推广到局部对称空间。

Provided that N is sectional curvature, K satisfies the local symmetrical complete Riemannian manifold of n ＋ p dimension of , M is n dimension compact submanifold of N with parallel average curvature vector, the submanifold is discussed, obtaining the rigid theorem about the reduction of square and codimension of second fundamental form, thus expanding the similar solution of curvature space to the local symmetrical space.