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Maximal space-like hypersurfaces in $H^4_1(-1)$ with zero Gauss-Kronecker curvature
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Abstract
In this paper, we study complete maximal space-like hypersurfaces with constant Gauss-Kronecker curvature in an anti-de Sitter space $\bold H^{4}_1(-1) $. It is proved that complete maximal space-like hypersurfaces with constant Gauss-Kronecker curvature in an anti-de Sitter space $\bold H^{4}_1(-1) $ are isometric to the hyperbolic cylinder $\bold H^{2}(c_1)\times \bold H^{1}(c_2)$ with $S=3$ or they satisfy $S\leq 2$, where $S$ denotes the squared norm of the second fundamental form.
참고문헌 (6)
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- "\ref \key 13 \by S. Nishikawa \paper On maximal space-like hypersurfaces in a Lorenzianmanifolds \jour Nagoya Math. J. \vol 95\pages 117--124\yr 1984\endref%" (1984)
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