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

Abstract

In this paper, we classify complete spacelike hypersurfaces in the anti-de Sitter space H 1 n + 1 ( − 1 ) ( n ⩾ 3 ) with constant scalar curvature and with two principal curvatures. Moreover, we prove that if M n 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 also obtain several rigidity theorems for such hypersurfaces.