On complete spacelike hypersurfaces with constant scalar curvature in the de Sitter space

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).