On spacelike hypersurfaces with constant scalar curvature in locally symmetric Lorentz spaces

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• 作者：Jiancheng Liu ; Zhongyang Sun
• 关键词：Locally symmetric Lorentz space ; Constant scalar curvature ; Spacelike hypersurface ; Second fundamental form
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2010
• 出版时间：1 April 2010
• 年：2010
• 卷：364
• 期：1
• 页码：195-203
• 全文大小：185 K

文摘

The purpose of this paper is to study compact or complete spacelike hypersurfaces with constant normalized scalar curvature in a locally symmetric Lorentz space satisfying some curvature conditions. We give an optimal estimate of the squared norm of the second fundamental form of such hypersurfaces. Furthermore, the totally umbilical hypersurfaces are characterized.