The pinching theorem for hypersurfaces of Minkowski spaces

Let ( M n , F ) be a compact Finsler hypersurface of a Minkowski space ( V n + 1 , F ¯ ) with constant mean curvature H. In this paper, using the Gauss formula of Chern connection for Finsler submanifolds, we prove that if the norm square S of the second fundamental form of M satisfies S ⩽ n 2 H 2 n − 1 , then M with the induced metric is isometric to the standard Euclidean sphere which was obtained by Kim (1997) [1] for the Riemannian case.