拟常曲率黎曼流形中具有平行平均曲率向量的子流形

拟常曲率黎曼流形中具有平行平均曲率向量的子流形

丁顺汉

丽水学院数学系，浙江省丽水 323000

收稿日期:2005-12-12 修回日期:1900-01-01 出版日期:2006-05-26 发布日期:2006-05-26
通讯作者: 丁顺汉

Compact Submanifolds in Quasi Constant CurvatureRiemannian Manifolds with Parallel Mean Curvature Vector

DING Shun-han

Department of Mathematics, Lishui College, Lishui 323000, Zhejiang Province, China

Received:2005-12-12 Revised:1900-01-01 Online:2006-05-26 Published:2006-05-26
Contact: DING Shun-han

摘要/Abstract

摘要： 研究拟常曲率黎曼流形中具有平行平均曲率向量的紧致子流形. 通过计算子流形第二基本形式模长平方的拉普拉斯, 利用Stokes定理, 得到这类子流形的一个积分不等式. 使得对拟常曲率黎曼流形中紧致子流形的研究由极小子流形和伪脐子流形情形扩展到具有平行平均曲率向量的情形.

关键词: 平行平均曲率, 黎曼流形, 紧致子流形

Abstract: The compact submanifolds in quasi constant curvature Riemannian manifolds with Parallel Mean Curature Vector were studied. By using Stokes theorem, and some last results of algebra inequation, an integral inequality was obtained. The work makes the study of compact submanifolds in quasi constantcurvature Riemannian manifolds extend from the especial case to general case.

Key words: parallel mean curvature, Riemannian manifold, compact submanifold

中图分类号:

O186.12

丁顺汉. 拟常曲率黎曼流形中具有平行平均曲率向量的子流形[J]. J4, 2006, 44(03): 380-384.

DING Shun-han. Compact Submanifolds in Quasi Constant CurvatureRiemannian Manifolds with Parallel Mean Curvature Vector[J]. J4, 2006, 44(03): 380-384.

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