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) over bar) 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. (C) 2011 Elsevier Inc. All rights reserved.