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Keywords:
Lorentzian space; spacelike hypersurface; the first eigenvalue; Gauss map
Lorentzian space; spacelike hypersurface; the first eigenvalue; Gauss map
Summary:
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.
References:
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