Finding umbilics on open convex surfaces
Francisco FonteneleUniversidade Federal Fluminense, Niterói, Brazil
Frederico XavierTexas Christian University, Fort Worth, USA
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. 2035–2052DOI 10.4171/RMI/1109