Landsberg hypersurfaces of Minkowski space with constant mean curvature

摘要

Let M ~n be a compact Landsberg hypersurface of Minkowski space (V ~(n+1), F?) with constant mean curvature H. In this paper, by the Gauss formula for the Chern connection, we establish the Simons integral inequality and prove that if the norm square S of the second fundamental form of M satisfies S < n ~2H ~2-1, then M is Riemannian with constant curvature.