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

Let M-n be a complete spacelike hypersurface with constant normalized scalar curvature R in the de Sitter Space S-1(n+1). Let H the mean curvature and suppose that (R) over bar = (R - 1) > 0 and (R) over bar less than or equal to sup H-2 less than or equal to C-(R) over bar, where C-(R) over bar is a constant depending only on R and n. It is proved that either sup H-2 = (R) over bar and M-n is totally umbilical, or sup H-2 = C-(R) over bar and M-n is the hyperbolic cylinder H-1(1 - coth(2) r) x Sn-1 (1 - tanh(2) r).