JournalsrmiVol. 35, No. 7pp. 2035–2052

Finding umbilics on open convex surfaces

  • Francisco Fontenele

    Universidade Federal Fluminense, Niterói, Brazil
  • Frederico Xavier

    Texas Christian University, Fort Worth, USA
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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\mathbb R^3 whose shape operator AA satisfies inf A>0|A|>0 and sup A<|\nabla A|<\infty.

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Francisco Fontenele, Frederico Xavier, Finding umbilics on open convex surfaces. Rev. Mat. Iberoam. 35 (2019), no. 7, pp. 2035–2052

DOI 10.4171/RMI/1109