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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.
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참고문헌 (6)
참고문헌 신청
/ 1967 / %\ref\key 14\by H. Omori \paper Isometric immersions of Riemannianmanifolds \jour J. Math. Soc. Japan \vol 19 \yr 1967 \pages205--214\endref%\ref\key 15\by B. O'Neil
/ 1975 / \ref\key 17 \by S. T. Yau \paper Harmonic functions on completeRiemannian manifolds \jour Comm. Pure Appl. Math. \vol 28 \yr1975 \pages 201--228
/ 1979 / 1--10\endref%\ref\key 8 \by S. Y. Cheng and S. T. Yau \paper Maximal space-likehypersurfaces in the Lorentz-Minkowski spaces \jour Ann. of Math. and J. E. Marsden\pa
/ 1984 / \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%
/ 1987 / \ref \key 1 \by K. Akutagawa\paper On space-like hypersurfaces with constant meancurvature in the de Sitter space \jour Math. Z. \vol 196\pages no. 1 13--19\yr 1987\
/ 1975 / \ref\key 17 \by S. T. Yau \paper Harmonic functions on completeRiemannian manifolds \jour Comm. Pure Appl. Math. \vol 28 \yr1975 \pages 201--228
/ 1979 / 1--10\endref%\ref\key 8 \by S. Y. Cheng and S. T. Yau \paper Maximal space-likehypersurfaces in the Lorentz-Minkowski spaces \jour Ann. of Math. and J. E. Marsden\pa
/ 1984 / \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%
/ 1987 / \ref \key 1 \by K. Akutagawa\paper On space-like hypersurfaces with constant meancurvature in the de Sitter space \jour Math. Z. \vol 196\pages no. 1 13--19\yr 1987\
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