A gap theorem for complete space-like hypersurface with constant scalar curvature in locally symmetric Lorentz spaces

Authors : Jiancheng LIU, Lin WEİ

Pages : 105-114

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Publication Date : 0000-00-00

Article Type : Research Paper

Abstract :Let Mn be a complete space-like hypersurface with constant scalar curvature in locally symmetric Lorentz space Nn+11, S be the squared norm of the second fundamental form of Mn in Nn+11. In this paper, we obtain a gap property of S: if nP\leq \sup S\leq Dinsert ignore into journalissuearticles values(n,P); for some constants P and Dinsert ignore into journalissuearticles values(n, P);, then either \sup S=nP and Mn is totally umbilical, or \sup S=Dinsert ignore into journalissuearticles values(n, P); and Mn has two distinct principal curvatures.
Keywords : Constant scalar curvature, space like hypersurface, second fundamental form, locally symmetric Lorentz space