On distance-preserving transformations of lines in Euclidean three-space
type: Item
instance of: scholarly article
title: On distance-preserving transformations of lines in Euclidean three-space
zbMATH Open document ID: 0555.51010
DOI: 10.1007/BF02189393
published in: Aequationes Mathematicae
publication date: 1985-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/137040
review text: The following theorem is proven: Fix \(\rho >0\) in R, and consider a bijection on the set of lines in Euclidean 3-space \(E_ 3\) such that the distance between two lines is \(\rho\) if and only if the distance between their images is \(\rho\). Then the bijection is induced by a motion of \(E_ 3\) (i.e. by an affine, distance-preserving bijection on \(E_ 3)\).
Mathematics Subject Classification ID: 51M05
Mathematics Subject Classification ID: 51M25
zbMATH DE Number: 3884868
zbMATH Keywords: motion of lines
zbMATH Keywords: Euclidean 3-space
author: June A. Lester
MaRDI profile type: Publication
cites work: Abstandsräume und eine einheitliche Definition verschiedener Geometrien
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description: scientific article; zbMATH DE number 3884868