Browse > Article
http://dx.doi.org/10.4134/BKMS.2012.49.2.271

LINEAR WEINGARTEN SPACELIKE HYPERSURFACES IN LOCALLY SYMMETRIC LORENTZ SPACE  

Yang, Dan (College of Sciences Shenyang University)
Publication Information
Bulletin of the Korean Mathematical Society / v.49, no.2, 2012 , pp. 271-284 More about this Journal
Abstract
Let M be a linear Weingarten spacelike hypersurface in a locally symmetric Lorentz space with R = aH + b, where R and H are the normalized scalar curvature and the mean curvature, respectively. In this paper, we give some conditions for the complete hypersurface M to be totally umbilical.
Keywords
linear Weingarten; spacelike hypersurface; locally symmetric;
Citations & Related Records
Times Cited By KSCI : 1  (Citation Analysis)  (Related Records In Web of Science)
연도 인용수 순위
1 M. Okumura, Hypersurfaces and a pinching problem on the second fundamental tensor, Amer. J. Math. 96 (1974), 207-213.   DOI   ScienceOn
2 J. Ramanathan, Complete spacelike hypersurfaces of constant mean curvature in de Sitter space, Indiana Univ. Math. J. 36 (1987), no. 2, 349-359.   DOI
3 S. C. Shu, Complete spacelike hypersurfaces in a de Sitter space, Bull. Austral. Math. Soc. 73 (2006), no. 1, 9-16.   DOI
4 S. C. Shu, Space-like hypersurfaces in locally symmetric Lorentz space, Anziam J. 50 (2008), no. 1, 1-11.   DOI   ScienceOn
5 Y. J. Suh, Y. S. Choi, and H. Y. Yang, On space-like hypersurfaces with constant mean curvature in a Lorentz manifold, Houston J. Math. 28 (2002), no. 1, 47-70.
6 S. C. Zhang and B. Q. Wu, Rigidity theorems for complete spacelike hypersurfaces with constant scalar curvature in locally symmetric Lorentz spaces, J. Geom. Phys. 60 (2010), no. 2, 333-340.   DOI   ScienceOn
7 F. E. C. Camargo, R. M. B. Chaves, and L. A. M. Sousa Jr, Rigidity theorems for complete spacelike hypersurfaces with constant scalar curvature in de Sitter space, Differential Geom. Appl. 26 (2008), no. 6, 592-599.   DOI   ScienceOn
8 A. Caminha, A rigidity theorem for complete CMC hypersurfaces in Lorentz manifolds, Differential Geom. Appl. 24 (2006), no. 6, 652-659.   DOI   ScienceOn
9 Q. M. Cheng, Complete space-like hypersurfaces of a de Sitter space with r = ${\kappa}H$, Mem. Fac. Sci. Kyushu Univ. Ser. A 44 (1990), no. 2, 67-77.   DOI
10 Q. M. Cheng and S. Ishikawa, Spacelike hypersurfaces with constant scalar curvature, Manuscripta Math. 95 (1998), no. 4, 499-505.   DOI   ScienceOn
11 A. J. Goddard, Some remarks on the existence of spacelike hypersurfaces of constant mean curvature, Math. Proc. Cambridge Philos. Soc. 82 (1977), no. 3, 489-495.   DOI   ScienceOn
12 H. Z. Li, Global rigidity theorems of hypersurfaces, Ark. Mat. 35 (1997), 327-351.   DOI   ScienceOn
13 H. Z. Li, Y. J. Suh, and G. X. Wei, Linear Weingarten hypersurfaces in a unit sphere, Bull. Korean Math. Soc. 46 (2009), no. 2, 321-329.   DOI   ScienceOn
14 J. C. Liu and Z. Y. Sun, On spacelike hypersurfaces with constant scalar curvature in locally symmetric Lorentz spaces, J. Math. Anal. Appl. 364 (2010), no. 1, 195-203.   DOI   ScienceOn
15 J. C. Liu and L. Wei, A gap theorem for complete space-like hypersurface with constant scalar curvature in locally symmetric Lorentz spaces, Turkish J. Math. 34 (2010), no. 1, 105-114.
16 S. Montiel, S. Montiel, An integral inequality for compact spacelike hypersurfaces in de Sitter space and applications to the case of constant mean curvature, Indiana Univ. Math. J. 37 (1988), no. 4, 909-917.   DOI
17 S. Montiel, A characterization of hyperbolic cylinders in the de Sitter space, Tohoku Math. J. (2) 48 (1996), no. 1, 23-31.   DOI
18 J. D. Baek, Q. M. Cheng, and Y. J. Suh, Complete space-like hypersurfaces in locally symmetric Lorentz spaces, J. Geom. Phys. 49 (2004), no. 2, 231-247.   DOI   ScienceOn
19 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.
20 K. Akutagawa, On spacelike hypersurfaces with constant mean curvature in the de Sitter space, Math. Z. 196 (1987), no. 1, 13-19.   DOI   ScienceOn
21 A. Brasil Jr, A. G. Colares, and O. Palmas, Complete hypersurfaces with constant scalar curvature in spheres, Monatsh. Math. 161 (2010), no. 4, 369-380.   DOI   ScienceOn