On Minkowski planes with transitive groups of homotheties
type: Item
instance of: scholarly article
title: On Minkowski planes with transitive groups of homotheties
zbMATH Open document ID: 0815.51013
DOI: 10.1007/BF02940791
published in: Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg
publication date: 1995-01-02T00:00:00Z
review text: In analogy with the well-known Lenz-Barlotti classification of projective planes, there are the Hering classification of Möbius planes [\textit{C. Hering}, Math. Z. 87, 252-262 (1965; Zbl 0126.166)], the Kleinewillinghofer classification of Laguerre planes [\textit{R. Kleinewillinghofer}, Arch. Math. 34, 469-480 (1980; Zbl 0457.51010)], and the Klein-Kroll classification of Minkowski planes [the authors, J. Geom. 36, No. 1/2, 99-109 (1989; Zbl 0694.51005)] which was later refined by the first author [J. Geom. 43, No. 1/2, 116-128 (1992; Zbl 0746.51009)]. A family \(M(r)\) of topological Minkowski planes was constructed by \textit{E. Hartmann} [Geom. Dedicata 10, 155-159 (1981; Zbl 0454.51004)]. A main result of the present work is that these planes \(M(r)\) of E. Hartmann (with \(r\) not 1) are completely characterized as the (necessarily infinite) locally compact, connected and finite dimensional Minkowski planes of class 19 (of the refined Klein-Kroll classification).
reviewed by: Stanley E. Payne
Mathematics Subject Classification ID: 51H15
Mathematics Subject Classification ID: 51B20
zbMATH DE Number: 706679
zbMATH Keywords: topological Minkowski planes
author: Monica Klein
author: Hans-Joachim Kroll
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf02940791
OpenAlex ID: W2018560404
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description: scientific article; zbMATH DE number 706679