Spacelike Hypersurfaces With Constant Scalar Curvature In H₁ⁿ⁺¹(c)

In this paper,we classify spacelike hypersurfaces in the anti-de Sitter space H₁ⁿ⁺¹(c) with constant scalar curvature and 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/n.Additionally,we prove several rigidity theorems for such hypersurfaces.