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

摘要

In this paper, we classify complete spacelike hypersurfaces in the anti-de Sitter space H1n+1(-1) (n≥) with constant scalar curvature and with two principal curvatures. Moreover, we prove that if Mn is a complete spacelike hypersurface with constant scalar curvature n(n-1)R and with two distinct principal curvatures such that the multiplicity of one of the principal curvatures is n-1, then R<(n-2)c. Additionally, we also obtain several rigidity theorems for such hypersurfaces.