Spacelike hypersurfaces of constant mean curvature with free boundary in Lorentzian space forms

In this paper we introduce a variational problem for spacelike hypersurface s in Lorentzian space forms whose critical points turn out to be constant m ean curvature spacelike hypersurfaces which intersect a given support hyper surface at a constant hyperbolic angle. For the two-dimensional case, when the support surface is totally umbilical we prove that only such surfaces a re totally umbilical too.