Galilei Laguerre geometry and rational circular offset surfaces
type: Item
instance of: scholarly article
title: Galilei Laguerre geometry and rational circular offset surfaces
zbMATH Open document ID: 0917.51003
author: J. Wallner
author: Horng-Yang Chen
author: Helmut Pottmann
published in: Beiträge zur Algebra und Geometrie
publication date: 1999-07-21T00:00:00Z
full work available at URL: https://eudml.org/doc/228423
full work available at URL: no.2
review text: The authors study the Laguerre geometry of the three-dimensional Galilei space. They investigate special models of this geometry (a cyclographic and an isotropic model with their duals) and its relevance for Laguerre transformations. These methods are used to construct ``rational circular offset surfaces \(\Psi\)'' of special given rational surfaces \(\Phi\): There the offset surface \(\Psi\) is generated by the Euclidean offset curves of the slices of \(\Phi\) in the parallel planes of a parallel bundle. The resulting surface \(\Psi\) then is an offset of \(\Phi\) with respect to a suitable chosen Galilei space and belongs to its Laguerre geometry. Then the authors give examples of rational circular offset surfaces (Galilei cyclides) and use them to model Galilei canal surfaces.
Mathematics Subject Classification ID: 51B15
Mathematics Subject Classification ID: 53A40
Mathematics Subject Classification ID: 68U07
zbMATH DE Number: 1208005
zbMATH Keywords: Galilei space
zbMATH Keywords: circular offset surfaces
zbMATH Keywords: cyclides of Galilei space
zbMATH Keywords: Laguerre geometry
reviewed by: Otto Röschel
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1208005