Hypersurfaces with prescribed curvatures in the de Sitter space

In this paper, we establish a relationship between spacelike hypersurfaces in the de Sitter space S(1)(n+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-1(n+1 ) satisfying certain global conditions and a very gen eral Weingarten relation W(k(1), ..., k(n) ) = 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.