Hypersurfaces of E_s⁴ with proper mean curvature vector

Abstract

Submanifolds satisfying Δ$¥vec H$=λ$¥vec H$ are named by B. Y. Chen submanifolds with proper mean curvature vector. We prove that a hypersurface of the pseudo-Euclidean space E_s⁴ with Δ$¥vec H$=λ$¥vec H$ and diagonalizable shape operator, has constant mean curvature.