A classification of biharmonic hypersurfaces in the Minkowski spaces of arbitrary dimension

In this paper we study hypersurfaces with the mean curvature function H satisfying 〈∇H; ∇H〉 = 0 in a Minkowski space of arbitrary dimension. First, we obtain some conditions satisfied by connection forms of biconservative hypersurfaces with the mean curvature function whose gradient is light-like. Then, we use these results to get a classification of biharmonic hypersurfaces. In particular, we prove that if a hypersurface is biharmonic, then it must have at least 6 distinct principal curvatures under the hypothesis of having mean curvature function satisfying the condition above.