局部对称共形平坦黎曼流形中具有平行平均曲率向量的子流形

本文把1]的结论推广到了环绕空间是局部对称共形平坦的情形,即获得了:设M~是局部对称共形平坦黎曼流形N~+p(p>1)中具有平行平均曲率向量的紧致子流形,如果则M~位于N~+p的全测地子流形N~+1中。其中S,H分别是M~的第二基本形式长度的平方和M~的平均曲率,T_C、t_c分别是N~+p的Ricci曲率的上、下确界,K是N~+p的数量曲率。

The Submanifolds with Parallel Mean Curvature Vector in a Locally Symmetric and Conformally Flat Riemannian Manifold

In the present paper we obtain the following result: Theorem Let M~R be a compact submanifold with parallel mean curvature vector in a locally symmetric and conformally flat Riemannian manifold N~(n+p)(p>1). If then M~n lies in a totally geodesic submanifold N~(n+1).