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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>2n 2|H|2/ (n− 1). Received: 28 November 2000 / Revised version: 7 May 2001
Keywords:Mathematics Subject Classification (2000): 53C42
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