Lines of curvature near umbilical points on surfaces immersed in \(\mathbb{R}^ 4\)
type: Item
instance of: scholarly article
title: Lines of curvature near umbilical points on surfaces immersed in \(\mathbb{R}^ 4\)
zbMATH Open document ID: 0836.53003
DOI: 10.1007/BF01120328
author: Federico Sánchez-Bringas
author: Ana Irene Ramírez-Galarza
published in: Annals of Global Analysis and Geometry
publication date: 1995-08-02T00:00:00Z
review text: The authors study the principal configurations (the set formed by umbilical points and families of lines of maximal and minimal curvatures) of pairs consisting of an immersion of a compact orientable surface in a 4-space and a smooth unitary vector field normal to the immersed surface. They prove a genericity theorem for certain types of pairs which are defined by the Darboux conditions at umbilical points.
Mathematics Subject Classification ID: 53A07
Mathematics Subject Classification ID: 37C75
Mathematics Subject Classification ID: 37G99
zbMATH DE Number: 780911
zbMATH Keywords: structural stability
zbMATH Keywords: principal configurations
zbMATH Keywords: umbilical points
reviewed by: V. D. Sedykh
MaRDI profile type: Publication
cites work: Q5678153
cites work: Positive Quadratic Differential Forms and Foliations with Singularities on Surfaces
cites work: The imbedding problem for Riemannian manifolds
cites work: Q3713216
full work available at URL: https://doi.org/10.1007/bf01120328
OpenAlex ID: W1501892490
description: scientific article; zbMATH DE number 780911