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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Abstract

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.

Cite this article

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