Biharmonic hypersurfaces of the 4-dimensional semi-Euclidean space

A submanifold of a semi-Euclidean space is said to have harmonic mean curvature vector field if , where 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 the shape operator of which is diagonalizable, with harmonic mean curvature vector field, is minimal.