A conformal mapping for a rectilinear congruence
type: Item
instance of: scholarly article
title: A conformal mapping for a rectilinear congruence
zbMATH Open document ID: 1116.53011
author: Despina Papadopoulou
published in: Journal of Geometry
publication date: 2007-01-24T00:00:00Z
review text: The author studies line congruences in a three-dimensional Euclidean space \(E^3\) with the property (c): the one-to-one mapping \(f: P(u, v)\to M(u, v)\), between their middle surface \(\overline{OP}= P(u, v)\) and their middle envelope \(\overline{OM}= M(u, v)\), is conformal. Apart from other interesting properties of them, it is proved that ``the determination of all congurences that have a given minimal surface \(M(u,v)\) as middle envelope and possess the property (c), is reduced to the integration of a non linear system of second order partial differential equations for an unknown function''. Additionally, in case \(M(u,v)\) is a right helicoid, the general solution of this system is found.
reviewed by: Pelagia Koltsaki
Mathematics Subject Classification ID: 53A25
zbMATH DE Number: 5118000
zbMATH Keywords: rectilinear congruences
zbMATH Keywords: middle surface
zbMATH Keywords: middle envelope
zbMATH Keywords: conformal mapping
MaRDI profile type: Publication
full work available at URL: s00022-006-0045-1
OpenAlex ID: W2005459251
DOI: 10.1007/S00022-006-0045-1
description: scientific article; zbMATH DE number 5118000