Finding umbilics on open convex surfaces

• Francisco Fontenele ^[1] ; Frederico Xavier ^[2]
  1. [1] Universidade Federal Fluminense

     Universidade Federal Fluminense

     Brasil

     
  2. [2] Texas Christian University

     Texas Christian University

     Estados Unidos

     
• Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 35, Nº 7, 2019, págs. 2035-2052
• Idioma: inglés
• DOI: 10.4171/rmi/1109
• Texto completo no disponible (Saber más ...)
• Resumen

  • By the Poincaré–Hopf theorem, every ovaloid has at least one umbilic. In this paper we extend this result to the more general case of complete positively curved surfaces in R3 whose shape operator A satisfies inf |A|>0 and sup |∇A|<∞.