Complete submanifolds in Euclidean spaces¶with parallel mean curvature vector

被引：1
|
作者：
Qing-Ming Cheng
Kazuhiro Nonaka
机构：
[1] Department of Mathematics,
[2] Faculty of Science and Engineering,undefined
[3] Saga University,undefined
[4] Saga 840-8502,undefined
[5] Japan. e-mail: Cheng@ms.saga-u.ac.jp,undefined
[6] Graduate School of Science,undefined
[7] Josai University,undefined
[8] Sakado,undefined
[9] Saitama 350-0295,undefined
[10] Japan,undefined
来源：
manuscripta mathematica | 2001年 / 105卷
关键词：
Mathematics Subject Classification (2000): 53C42;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
In this paper, we prove that n-dimensional complete and connected submanifolds with parallel mean curvature vector H in the (n+p)-dimensional Euclidean space En+p are the totally geodesic Euclidean space En, the totally umbilical sphere Sn (c) or the generalized cylinder Sn− 1 (c) ×E1 if the second fundamental form h satisfies <h>2≤n2|H|2/ (n− 1).
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页码：353 / 366
页数：13
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