具有正截面曲率的子流形的几何与拓扑

Geometry and Topology of Submanifolds with Positive Sectional Curvature

设Mm是空间形式Nn(c)中具有正截面曲率的紧致子流形,证明了如果n-m≥2,Mm的平均曲率向量关于法联络平行且不为零,则在Mm中不存在稳定积分流,且Mm的同调群消没。

Let M^mbe a compact submanifold with positive sectional curvature of a space form N^n （c）. It is showed that if n - m≥2 and M^m is of nonzero parallel mean curvature vector, then there are no stable integral currents in M^m and the homology groups of M^m vanish.