On complete spacelike hypersurfaces with constant scalar curvature in the de Sitter space - BRASIL JR,ALDIR (2000)
Let Mn be a complete spacelike hypersurface with constant normalized scalar curvature R in the de Sitter Space S1n + 1. Let H the mean curvature and suppose that = (R - 1) > 0 and <= sup H² <= C , where C is a constant depending only on R and n. It is proved that either sup H² = and Mn is totally umbilical, or sup H² = C and Mn is the hyperbolic cylinder H¹(1 - coth²r) x Sn - 1 (1 - tanh²r).