Geodesic
Characterization of hyperbolic cylinders in a Lorentzian space form
Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 8 (2012) no. 1, pp. 79-89 Cet article a éte moissonné depuis la source Math-Net.Ru

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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 $\lambda<\mu$. 
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Shichang Shu; Annie Yi Han. Characterization of hyperbolic cylinders in a Lorentzian space form. Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 8 (2012) no. 1, pp. 79-89. http://geodesic.mathdoc.fr/item/JMAG_2012_8_1_a4/

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