Geodesic
On the first eigenvalue of spacelike hypersurfaces in Lorentzian space
Archivum mathematicum, Tome 42 (2006) no. 3, pp. 233-238
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In this paper we obtain a lower bound for the first Dirichlet eigenvalue of complete spacelike hypersurfaces in Lorentzian space in terms of mean curvature and the square length of the second fundamental form. This estimate is sharp for totally umbilical hyperbolic spaces in Lorentzian space. We also get a sufficient condition for spacelike hypersurface to have zero first eigenvalue.
In this paper we obtain a lower bound for the first Dirichlet eigenvalue of complete spacelike hypersurfaces in Lorentzian space in terms of mean curvature and the square length of the second fundamental form. This estimate is sharp for totally umbilical hyperbolic spaces in Lorentzian space. We also get a sufficient condition for spacelike hypersurface to have zero first eigenvalue.
Classification : 53C40, 53C50, 58J50
Keywords: Lorentzian space; spacelike hypersurface; the first eigenvalue; Gauss map 
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Wu, Bing-Ye. On the first eigenvalue of spacelike hypersurfaces in Lorentzian space. Archivum mathematicum, Tome 42 (2006) no. 3, pp. 233-238. http://geodesic.mathdoc.fr/item/ARM_2006_42_3_a3/

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