On Complete Spacelike Hypersurfaces with Constant Scalar Curvature in the De Sitter Space

presented by Manfredo do Carmo Let Mn be a complete spacelike hypersurface with constant normalized scalar curvature R in the de Sitter Space Sn+11. Let H the mean curvature and suppose that R = (R − 1)> 0 and R ≤ supH 2 ≤ CR, where CR is a constant depending only on R and n. It is proved that either supH 2 = R and Mn is totally umbilical, or supH 2 = CR and Mn is the hyperbolic cylinder H 1(1 − coth2 r) × Sn−1(1 − tanh2 r). Key words: hyperbolic cylinder, spacelike hypersurfaces, de Sitter space. 1