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

We classify spacelike hypersurfaces of the de Sitter space S1n+1(c) with constant scalar curvature and with two principal curvatures. Moreover, we prove that if MnMn is a complete spacelike hypersurface with constant scalar curvature n(n−1)Rn(n−1)R and with two distinct principal curvatures such that the multiplicity of one of the principal curvatures is n−1n−1, then R<(n−2)c/nR<(n−2)c/n. Additionally, we prove several rigidity theorems for such hypersurfaces.