Abstract
A Riemannian manifold Mn isometrically immersed into a Euclidean space Em with the mean curvature vector H→ is said to have a proper mean curvature vector field (with respect to the action of the Laplacian Δ of the induced metric on Mn) if it satisfies ΔH→=αH→ for α∈R. In this paper, we prove that every hypersurface of E5 with ΔH→=αH→ has constant mean curvature and constant scalar curvature.
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