Finding umbilics on open convex surfaces
Francisco Fontenele
Universidade Federal Fluminense, Niterói, BrazilFrederico 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 whose shape operator satisfies inf and sup .
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