Structurally stable configurations of lines of mean curvature and umbilic points on surfaces immersed in \(\mathbb{R}^3\)
type: Item
instance of: scholarly article
title: Structurally stable configurations of lines of mean curvature and umbilic points on surfaces immersed in \(\mathbb{R}^3\)
zbMATH Open document ID: 1005.53003
DOI: 10.5565/PUBLMAT_45201_08
author: Ronaldo A. Garcia
author: Jorge Sotomayor
published in: Publicacions Matemàtiques
publication date: 2003-02-16T00:00:00Z
full work available at URL: https://eudml.org/doc/41438
review text: The present paper concerns the mean curvature configurations associated to immersions of an oriented surface into \(\mathbb{R}^3\), i.e. pairs of orthogonal foliations whose singularities and leaves are given respectively by the umbilic points and the lines of normal mean curvature of the immersion. These lines are characterized by the condition that along them the immersions bend according to their normal mean curvature. Using the formal analogy between mean and principal configurations, the authors study the stable and generic cases of umbilic points and mean curvature cycles, providing in this way sufficient conditions for mean curvature structural stability. Moreover, examples of mean curvature configurations on the ellipsoid and torus are given.
reviewed by: Anna Fino
Mathematics Subject Classification ID: 53A07
Mathematics Subject Classification ID: 53A05
zbMATH DE Number: 1740176
zbMATH Keywords: umbilic point
zbMATH Keywords: mean curvature configuration
zbMATH Keywords: lines of mean curvature
MaRDI profile type: Publication
OpenAlex ID: W2134255336
description: scientific article; zbMATH DE number 1740176