Finding umbilics on open convex surfaces

  title={Finding umbilics on open convex surfaces},
  author={Francisco Fontenele and Frederico Xavier},
  journal={Revista Matem{\'a}tica Iberoamericana},
By the Poincare–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|<∞. 

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