Semiclassical topological flat Laguerre planes obtained by pasting along two parallel classs
type: Item
instance of: scholarly article
title: Semiclassical topological flat Laguerre planes obtained by pasting along two parallel classs
zbMATH Open document ID: 0659.51021
DOI: 10.1007/BF01222526
published in: Journal of Geometry
publication date: 1988-01-01T00:00:00Z
review text: A topological flat Laguerre plane is called semiclassical if its point space is the union of two closed halfplanes whose induced subgeometries are both isomorphic to their classical counterparts. The intersection of these two halfplanes consists of either two parallel classes or one circle. Here the author investigates the first possibility whereas he discusses the second one in Result Mat. 12, 207-221 (1987; Zbl 0632.51018). Any semiclassical flat Laguerre plane of the first kind can be constructed with the aid of three orientation preserving homeomorphisms of \({\mathbb{R}}\) fixing 0 and vice versa. The author determines the isomorphism classes and the collineation groups of the planes under consideration. In most cases the automorphism group turns out to be 0-dimensional or even trivial but for suitably chosen generating functions its dimension can take on all possible values.
Mathematics Subject Classification ID: 51H15
Mathematics Subject Classification ID: 51B15
zbMATH DE Number: 4078141
zbMATH Keywords: flat Laguerre plane
zbMATH Keywords: isomorphism classes
zbMATH Keywords: collineation groups
author: Günter F. Steinke
reviewed by: Norbert Knarr
MaRDI profile type: Publication
cites work: Laguerre and Minkowski planes produced by dilatations
cites work: Q5674022
cites work: Topologische Laguerreebenen. I
cites work: Topologische Laguerreebenen, II
cites work: Characterization of ovoidal Laguerre planes
cites work: Moulton-Laguerre-Ebenen
cites work: Eine Klasse nicht einbettbarer reeller Laguerre-Ebenen
cites work: Transitivitaetsaetze für Laguerre-Ebenen
cites work: Q5339349
cites work: Topological planes
cites work: An extension property for classical topological Benz planes
cites work: The automorphism group of Laguerre planes. (Complement to: The automorphism group of locally compact connected topological Benz planes)
cites work: Topological affine planes composed of two desarguesian halfplanes and projective planes with trivial collineation group
cites work: Semiclassical topological Möbius planes
cites work: Semiclassical topological flat Laguerre planes obtained by pasting along a circle
full work available at URL: https://doi.org/10.1007/bf01222526
OpenAlex ID: W2152723445
description: scientific article; zbMATH DE number 4078141