Hypersurfaces with prescribed curvatures in the de Sitter space

• Ángela Roldán ^[1]
  1. [1] Universidad de Córdoba

     Universidad de Córdoba

     Cordoba, España

     
• Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 38, Nº 1, 2022, págs. 269-294
• Idioma: inglés
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• Resumen

  • 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.