Complete space-like hypersurfaces in locally symmetric Lorentz spaces

The purpose of this paper is to study complete space-like hypersurfaces with constant mean 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 total...

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Bibliographic Details
Published in:Journal of geometry and physics 2004-02, Vol.49 (2), p.231-247
Main Authors: Ok Baek, Jin, Cheng, Qing-Ming, Jin Suh, Young
Format: Article
Language:English
Subjects:
Constant mean curvature
Locally symmetric Lorentz space
Second fundamental form
Space-like hypersurface
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Summary:The purpose of this paper is to study complete space-like hypersurfaces with constant mean 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.
ISSN:0393-0440
1879-1662
DOI:10.1016/S0393-0440(03)00090-1