The pinching theorem for hypersurfaces of Minkowski spaces
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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)  for the Riemannian case. (C) 2011 Elsevier Inc. All rights reserved.
CitationJOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS,2012,388（2）：1285-1291