具有平行平均曲率向量场的子流形

SUBMANIFOLDS WITH PARALLEL MEAN CURVATURE VECTOR FIELD

本文改进了 S.T.Yau(文[1])中关于单位球面中具有平行平均曲率向量场的子流形的一个结果。然而从截面曲率这一角度出发,给出了空间形式 R^(n+p)(c)(n>1,p>1)中具有平行平均曲率向量场的可定向闭子流形 M^n 的有关结果和积分不等式.

In this paper,we improved a result S.T.Yau[1],then obtained someresults and unequalities on the sectional curvature of the oriented closedsubmanifolds M^n with parallel mean curvature vector of a space form R^(n+p)(c)(n>1,p>1).