Lines of curvature of algebraic surfaces
type: Item
instance of: scholarly article
title: Lines of curvature of algebraic surfaces
zbMATH Open document ID: 0871.53007
published in: Bulletin des Sciences Mathématiques
publication date: 1997-08-21T00:00:00Z
review text: Let \(S\subset{\mathbb R}^3\) be a real algebraic surface. At each smooth point of \(S\), where the two principal curvatures are different, consider the two orthogonal principal curvature directions. The corresponding integral curves on \(S\) are the lines of minimal and maximal principal curvature. The surface \(S\) is called structurally stable, if for every small perturbation \(S'\) of \(S\), there is a homeomorphism between \(S\) and \(S'\), which maps the lines of minimal and maximal principal curvature of \(S\) onto those of \(S'\). The authors prove that a generic surface of degree \(d\geq3\) is structurally stable.
Mathematics Subject Classification ID: 53A05
Mathematics Subject Classification ID: 14P05
zbMATH DE Number: 1013720
zbMATH Keywords: real algebraic surfaces
zbMATH Keywords: principal curvature
zbMATH Keywords: stability
author: Jorge Sotomayor
author: Ronaldo A. Garcia
reviewed by: Stefan Helmke
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1013720