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http://dx.doi.org/10.4134/BKMS.2010.47.5.1067

ON COMPLETE SPACELIKE (r-1)-MAXIMAL HYPERSURFACES IN THE ANTI-DE SITTER SPACE H1n+1  

Yang, Biaogui (SCHOOL OF MATHEMATICS AND COMPUTER SCIENCES FUJIAN NORMAL UNIVERSITY)
Publication Information
Bulletin of the Korean Mathematical Society / v.47, no.5, 2010 , pp. 1067-1076 More about this Journal
Abstract
In this paper we investigate complete spacelike (r - 1)-maximal (i.e., $H_r\;{\equiv}\;0$) hypersurfaces with two distinct principal curvatures in the anti-de Sitter space $\mathbb{H}_1^{n+1}$(-1). We give a characterization of the hyperbolic cylinder.
Keywords
spacelike hypersurface; (r - 1)-maximal; anti-de Sitter space; hyperbolic cylinder; generalized maximum principle;
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1 S.-Y. Cheng and S.-T. Yau, Hypersurfaces with constant scalar curvature, Math. Ann. 225 (1977), no. 3, 195-204.   DOI
2 T. Ishihara, Maximal spacelike submanifolds of a pseudo-Riemannian space of constant curvature, Michigan Math. J. 35 (1988), no. 3, 345-352.   DOI
3 Z.-Q. Li and X.-H. Xie, Space-like isoparametric hypersurfaces in Lorentzian space forms, Front. Math. China 1 (2006), no. 1, 130-137.   DOI   ScienceOn
4 H. Omori, Isometric immersions of Riemannian manifolds, J. Math. Soc. Japan 19 (1967), 205-214.   DOI
5 B. O’Neill, Semi-Riemannian Geometry with Appications to Relativity, Academic Press, New York, 1983.
6 G.-X. Wei, Rigidity theorem for hypersurfaces in a unit sphere, Monatsh. Math. 149 (2006), no. 4, 343-350.   DOI
7 S.-T. Yau, Harmonic functions on complete Riemannian manifolds, Comm. Pure Appl. Math. 28 (1975), 201-228.   DOI
8 B.-G. Yang and X.-M. Liu, Complete Spacelike hypersurfaces with constant mean curvature in an anti-de Sitter space, Front. Math. China. 4 (2009), no. 4, 727-737.   DOI   ScienceOn
9 N. Abe, N. Koike, and S. Yamaguchi, Congruence theorems for proper semi-Riemannian hypersurfaces in a real space form, Yokohama Math. J. 35 (1987), no. 1-2, 123-136.
10 L.-F. Cao and G.-X. Wei, A new characterization of hyperbolic cylinder in anti-de Sitter space $H_1^{n+1}$(-1), J. Math. Anal. Appl. 329 (2007), no. 1, 408-414.   DOI   ScienceOn