Address.
Department of Mathematics, Minjiang University,
Fuzhou, Fujian, 350108, P.
R. China
E-mail. bingyewu@yahoo.com.cn
Abstract.
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.
AMSclassification. Primary 53C42; Secondary 53B30.
Keywords. Lorentzian space, spacelike hypersurface, the first eigenvalue, Gauss map.