Complete submanifolds in Euclidean spaces¶with parallel mean curvature vector |
| |
Authors: | Qing-Ming Cheng Kazuhiro Nonaka |
| |
Institution: | (1) Department of Mathematics, Faculty of Science and Engineering, Saga University, Saga 840-8502, Japan. e-mail: Cheng@ms.saga-u.ac.jp, JP;(2) Graduate School of Science, Josai University, Sakado, Saitama 350-0295, Japan, JP |
| |
Abstract: | 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 E
n
+
p
are the totally geodesic Euclidean space E
n
, the totally umbilical sphere S
n
(c) or the generalized cylinder S
n
− 1 (c) ×E
1 if the second fundamental form h satisfies <h>2≤n
2|H|2/ (n− 1).
Received: 28 November 2000 / Revised version: 7 May 2001 |
| |
Keywords: | Mathematics Subject Classification (2000): 53C42 |
本文献已被 SpringerLink 等数据库收录! |
|