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

Authors : Jiancheng Liu, Lin Wei

Pages : 105-114

View : 14 | Download : 8

Publication Date : 9999-12-31

Article Type : Makaleler

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 D(n,P) for some constants P and D(n, P), then either \sup S=nP and Mn is totally umbilical, or \sup S=D(n, P) and Mn has two distinct principal curvatures.
Keywords : Constant scalar curvature, space-like hypersurface, second fundamental form, locally symmetric Lorentz space.