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

Jiancheng LIU
Department of Mathematics, Northwest Normal University,
Lanzhou 730070, CHINA
e-mail: liujc@nwnu.edu.cn [1ex]
Lin WEI
Department of Mathematics, Northwest Normal University,
Lanzhou 730070, CHINA
e-mail: weilin0312@163.com

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.

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

Turk. J. Math., 34, (2010), 105-114.
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Other articles published in the same issue: Turk. J. Math.,vol.34,iss.1.