On conditions for existence of umbilical points on a convex surface
type: Item
instance of: scholarly article
title: On conditions for existence of umbilical points on a convex surface
zbMATH Open document ID: 0856.53006
DOI: 10.1007/BF02107335
published in: Siberian Mathematical Journal
publication date: 1996-10-15T00:00:00Z
review text: Let \(F\) be a connected complete \(C^\infty\) surface homeomorphic to a plane in the Euclidean space \(\mathbb{R}^3\) and \(k_1\), \(k_2\) its principal curvatures. The author establishes the following result. If the surface \(F\) satisfies one of the following conditions: (i) the integral curvature is strictly smaller than \(2\pi\), (ii) the Gauss curvature and the modules of the gradient functions for \(k_1\) and \(k_2\) are bounded on \(F\); then \(\inf_{p\in F} (k_2(p)-k_1(p))=0\).
Mathematics Subject Classification ID: 53A05
Mathematics Subject Classification ID: 53C40
zbMATH DE Number: 923546
zbMATH Keywords: connected complete surface
zbMATH Keywords: principal curvatures
zbMATH Keywords: integral curvature
zbMATH Keywords: Gauss curvature
reviewed by: Vasile Cruceanu
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1007/bf02107335
OpenAlex ID: W2023512923
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description: scientific article; zbMATH DE number 923546