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Zhurnal Matematicheskoi Fiziki, Analiza, Geometrii [Journal of Mathematical Physics, Analysis, Geometry], 2012, Volume 8, Number 1, Pages 79–89
(Mi jmag526)
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Characterization of hyperbolic cylinders in a Lorentzian space form
Shichang Shua, Annie Yi Hanb a Department of Mathematics, Xianyang Normal University Xianyang, 712000, Shaanxi, P. R. China
b Department of Mathematics, Borough of Manhattan Community College CUNY 10007 New York USA
Abstract:
We give a characterization of the $n$-dimensional ($n\geq3$) hyperbolic cylinders in a Lorentzian space form. We show that the hyperbolic cylinders are the only complete space-like hypersurfaces in an $(n+1)$-dimensional Lorentzian space form $M^{n+1}_1(c)$ with non-zero constant mean curvature $H$ whose two distinct principal curvatures $\lambda$ and $\mu$ satisfy $\inf(\lambda-\mu)^2>0$ for $c\leq 0$ or $\inf(\lambda-\mu)^2>0$, $H^2\geq c$, for $c> 0$, where $\lambda$ is of multiplicity $n-1$ and $\mu$ of multiplicity $1$ and $\lambda<\mu$.
Key words and phrases:
space-like hypersurface, Lorentzian space form, mean curvature, principal curvature, hyperbolic cylinder.
Received: 08.01.2009
Citation:
Shichang Shu, Annie Yi Han, “Characterization of hyperbolic cylinders in a Lorentzian space form”, Zh. Mat. Fiz. Anal. Geom., 8:1 (2012), 79–89
Linking options:
https://www.mathnet.ru/eng/jmag526 https://www.mathnet.ru/eng/jmag/v8/i1/p79
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Abstract page: | 237 | Full-text PDF : | 69 | References: | 29 |
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