Simple umbilics revisited
type: Item
instance of: scholarly article
title: Simple umbilics revisited
zbMATH Open document ID: 0999.53002
DOI: 10.1016/S0926-2245(00)00034-6
author: Igor V. Nikolaev
published in: Differential Geometry and its Applications
publication date: 2002-12-05T00:00:00Z
review text: This paper deals with an old result of Cayley and Darboux concerning the topological classification of simple umbilical points of a smooth surface in \(E^3\), i.e. umbilical points which cannot be broken into simpler by a small deformation of the surface. The author proves among others the following stability theorem: The 3-jet of the germ at an isolated simple umbilical point is topologically sufficient. Furthermore, the configuration of the lines of principal curvature in the neighborhood of such an umbilical point belongs to exactly one of four classes called ``tripod'', ``sunset'', ``degenerate sunset'' and ``thorn''.
Mathematics Subject Classification ID: 53A05
Mathematics Subject Classification ID: 57R30
zbMATH DE Number: 1567207
zbMATH Keywords: umbilical point
zbMATH Keywords: foliation
zbMATH Keywords: structural stability
reviewed by: Stylianos Stamatakis
MaRDI profile type: Publication
Wikidata QID: Q115338367
cites work: Singularities of vector fields on the plane
cites work: Q4051278
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description: scientific article; zbMATH DE number 1567207