具有平行平均曲率向量场的H稳定子流形  

H-Stable Submanifolds with Parallel Mean Curvature Vector Field

作　　者：李中林[1] 

机构地区：[1]杭州大学数学系

出　　处：《杭州大学学报（自然科学版）》1989年第3期237-244,共8页Journal of Hangzhou University Natural Science Edition

基　　金：中国科学院科学基金资助课题

摘　　要：本文讨论局部对称共形平坦Riemann流形N中的紧致H稳定子流形M,若M具于平行平均曲率向量场,则对M的截面曲率或Ricci曲率加上适当的限制条件后,我们证明了M是N中某全脐点子流形N^(N+1)的全脐点超曲面。In this paper, we establish the following theorems. Theorem 1. Let N be an (n + p)-dimensional locally symmetric, con-formally flat Riemannian manifold and M a p(>1)-codimensional compact H-stable submanifold immersed in N. If M is pseudo-umbilical with parallel mean curvature vector field and if the sectional curvature of M is greater than everywhere on M, then M is a totally umbilical hypersurface in an (n+1)-dimensional totally umbilical submanifold of N. Theorem 2. Suppose that N and M satisfy the condition of the theorem 1 with p≥1. If either the Ricci curvature of M is greater than or the Ricci curvature of M is not less than everywhere on M, then M is a totally umbilical hypersurface in an (n+1)-dimensional totally umbilical submanifold of N .

关 键 词：黎曼流形 H稳定子流形 局部对称 

分 类 号：O186.12[理学—数学]