关于具有平行平均曲率向量子流形

ON SUBMANIFOLDS WITH PARALLEL MEAN CURVATURE VECTOR

本文研究一般黎曼流形中具有平行平均曲率向量的子流形,得到了关于这类子流形的一个积分不等式及相应的一个余维数减小的定理,推广了S.T.Yau的一个结论.

In this paper, we discuss submanifolds with parallel mean curvature vector in riemannian manifold. We prove an integral inequality and a theorem about the reduction of the codimension, which generalizes the result due to S. T. Yan.