Hypersurfaces satisfying [formula omitted] in [formula omitted

Abstract

In this paper, we study hypersurfaces Mr4(r=0,1,2,3,4) satisfying △H→=λH→ (λ a constant) in the pseudo-Euclidean space Es5(s=0,1,2,3,4,5). We obtain that every such hypersurface in Es5 with diagonal shape operator has constant mean curvature, constant norm of second fundamental form and constant scalar curvature. Also, we prove that every biharmonic hypersurface in Es5 with diagonal shape operator must be minimal.