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).
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Received: 28 November 2000 / Revised version: 7 May 2001
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Cheng, QM., Nonaka, K. Complete submanifolds in Euclidean spaces¶with parallel mean curvature vector. manuscripta math. 105, 353–366 (2001). https://doi.org/10.1007/s002290100186
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DOI: https://doi.org/10.1007/s002290100186