Complete maximal space-like hypersurfaces in an anti-de Sitter space of dimension 4

Let Rn+11 be an (n+1)-demensional Minkowski space and Sn-ii(c) (resp. Hn+11(c)9 and (n÷1)-demensional de Sitter space (resp. an anti-de Sitter space) of constant curvature c. The class of these indefinite Riemannian manifolds of constant curvature c and with index 1 is called a Lorentz space form, ..