Resumen de Hypersurfaces with prescribed curvatures in the de Sitter space

Ángela Roldán

• In this paper, we establish a relationship between spacelike hypersurfaces in the de Sitter space Sn+11 and conformal metrics on the sphere Sn. As a consequence of this relation and some deep results in conformal geometry, we classify spacelike hypersurfaces in Sn+11 satisfying certain global conditions and a very general Weingarten relation W(k1,…,kn)=0 of elliptic type, where k1,…,kn are its principal curvatures. Also, we particularize to some important cases as the rth mean curvatures.