The pinching theorem for hypersurfaces of Minkowski spaces

Abstract

Let (Mn,F) be a compact Finsler hypersurface of a Minkowski space (Vn+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⩽n2H2n−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.