Darboux curves on surfaces I
type: Item
instance of: scholarly article
title: Darboux curves on surfaces I
zbMATH Open document ID: 1391.53011
author: Rémi Langevin
author: Ronaldo A. Garcia
author: Paweł Walczak
published in: Journal of the Mathematical Society of Japan
publication date: 2017-04-05T00:00:00Z
full work available at URL: https://projecteuclid.org/euclid.jmsj/1484730016
review text: In this paper a class of curves on a surface is investigated. These curves are characterized by the property that their osculating spheres are tangent to the surface. Such curves are referred to as `Darboux curves'. In this paper Darboux curves are characterized under the Lorentz group. This way, such curves can even be described as geodesics in a 3-dimensional sub-variety of some quadric. This thorough investigation of such curves is based on the space of oriented spheres which can be viewed as a hyperquadric of the 5-dimensional Lorentz space.
reviewed by: Johann Lang
Mathematics Subject Classification ID: 53A30
Mathematics Subject Classification ID: 53C12
Mathematics Subject Classification ID: 53C50
Mathematics Subject Classification ID: 57R30
zbMATH DE Number: 6701581
zbMATH Keywords: Darboux curve
zbMATH Keywords: canal surface
zbMATH Keywords: conformal geometry
zbMATH Keywords: space of spheres
zbMATH Keywords: Lorentz group
MaRDI profile type: Publication
OpenAlex ID: W2573931504
DOI: 10.2969/JMSJ/06910001
description: scientific article; zbMATH DE number 6701581