Hypersurfaces with prescribed curvatures in the de Sitter space (Q832444)

Summary: In this paper, we establish a relationship between spacelike hypersurfaces in the de Sitter space \(\mathbb{S}_1^{n+1}\) and conformal metrics on the sphere \(\mathbb{S}^n\). As a consequence of this relation and some deep results in conformal geometry, we classify spacelike hypersurfaces in \(\mathbb{S}_1^{n+1}\) satisfying certain global conditions and a very general Weingarten relation \(W(k_1,\dots,k_n)= 0\) of elliptic type, where \(k_1,\dots,k_n\) are its principal curvatures. Also, we particularize to some important cases as the \(r\)th mean curvatures.