常曲率空间中具有平行平均曲率向量子流形的不等式

An inequality on submanifolds with parallel mean curvature vector in a space of constant curvature

设Mn是等距浸入在常曲率黎曼流形Nn+p(c)中的n维紧致子流形,若Mn是极小的,有著名的Simons不等式.李安民等人改进了此不等式,现在进一步把它推广到常曲率黎曼流形的具有平行平均曲率的子流形的情形.

Let N^n＋p （c）be an n＋ p dimensional Riemannian manifold with constant curvature c and M^n an n dimensional compact submanifold of N^n＋P（c）. It is known that there is a Simons＇ inequality when M＂ is minimal. Li An Min etc. improved this inequality. Now this paper gives the generalizations of the inequality for the case that the mean curvature vector field of M^n is parallel.