Lin WEI, Jiancheng LIU

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

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.

Anahtar Kelimeler:

Constant scalar curvature, space-like hypersurface, second fundamental form, locally symmetric Lorentz space.

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

Keywords:

Constant scalar curvature, space-like hypersurface, second fundamental form, locally symmetric Lorentz space.,

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Department of Mathematics, Northwest Normal University, Lanzhou 730070, CHINA e-mail: liujc@nwnu.edu.cn Lin WEI
Department of Mathematics, Northwest Normal University, Lanzhou 730070, CHINA e-mail: weilin 0312@163.com