A classification theorem for hypersurfaces of Minkowski space

Abstract

Let Mn be a compact hypersurface of a Minkowski space (Vn+1, F). In this paper, using the Gauss formula of the Chern connection for Finsler submanifolds, we prove that if the second mean curvature H2 of M is constant and the norm square S of the second fundamental form of M satisfies S  n(n−1) n−2 H2, then M with the induced metric is isometric to the standard Euclidean sphere. This generalizes the result of [2] from the Euclidean to the Minkowski space.