常曲率空间中具有相同常平均曲率的黎曼叶状结构

A Riemannian Foliation with Paralel Mean Curvature on a Riemannian Manifold

设M是一个紧可定向流形,F为M上的黎曼叶状结构,它被许多几何学家所关注.论文研究的是常曲率空间中具有相同常平均曲率的黎曼叶状结构.借鉴文献[1]中的证明方法,利用Nakagawa和Takagi[2]的计算散度的方法,并且结合有关常曲率空间中具有平行平均曲率的子流形的最新Pingching结果,证明了一个Simons型的Pinching定理.

The purpose of this paper is to study a Riemannian foliation with parallel mean curvature on a Riemannian manifold. The author used the method of Nakagawa and Takagi to calculate divergenence of a vector field[2] ,after S. T. Yau [1]and some last pinching result about submanifolds with parallel mean curvature in the space with constant curnature,obtained a formula of Simons type.