Complete submanifolds in Euclidean spaces with parallel mean curvature vector

In this paper, we prove that n-dimensional complete and connected sub manif olds with parallel mean curvature vector H in the (n+p)-dimensional Euclide an space En+p are the totally geodesic Euclidean space E-n, the totally umb ilical sphere S-n(c) or the generalized cylinder Sn-1(c) x E-1 if the secon d fundamental form h satisfies [h](2) less than or equal to n(2)\H\(2)/(n - 1).