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 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 2≤n2|H|2/ (n− 1).
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