No abstract

In this paper, we establish a relationship between spacelike hypersurfaces in the de Sitter space S nC1 1 and conformal metrics on the sphere S n . As a consequence of this relation and some deep results in conformal geometry, we classify spacelike hypersurfaces in S nC1 1 satisfying certain global conditions and a very general Weingarten relation W .k 1 ; : : : ; k n / D 0 of elliptic type, where k 1 ; : : : ; k n are its principal curvatures. Also, we particularize to some important cases as the rth mean curvatures.