Biharmonic hypersurfaces of the 4-dimensional semi-Euclidean space Es4

Abstract

A submanifold Mrn of a semi-Euclidean space Esm is said to have harmonic mean curvature vector field if ΔH→ = 0→, where H→ denotes the mean curvature vector; submanifolds with harmonic mean curvature vector are also known as biharmonic submanifolds. In this paper, we prove that every nondegenerate hypersurface of Es4 the shape operator of which is diagonalizable, with harmonic mean curvature vector field, is minimal. © 2005 Elsevier Inc. All rigths reserved.