A note on the Kleinewillinghöfer types of 4-dimensional Laguerre planes-Reference-Cited by-同舟云学术

A note on the Kleinewillinghöfer types of 4-dimensional Laguerre planes

Published:2022-10-01 Issue:4 Volume:22 Page:579-590
ISSN:1615-7168
Container-title:Advances in Geometry
language:en
Short-container-title:

Author:

Steinke Günter F.¹

Affiliation:

1. School of Mathematics and Statistics, University of Canterbury , Private Bag 4800 , Christchurch , New Zealand

Abstract

Abstract Kleinewillinghöfer classified in 1979 automorphism groups of Laguerre planes with respect to linearly transitive subgroups of central automorphisms and obtained a multitude of types. All feasible Kleinewillinghöfer types of 2-dimensional Laguerre planes were completely determined in 2021. In this paper we investigate the Kleinewillinghöfer types of 4-dimensional Laguerre planes with respect to the automorphism groups of these planes and show that of the 49 types Kleinewillinghöfer described, only twelve are feasible in 4-dimensional Laguerre planes. Examples of four of these type are provided.

Publisher

Walter de Gruyter GmbH

Subject

Geometry and Topology

Link

https://www.degruyter.com/document/doi/10.1515/advgeom-2022-0020/pdf

Reference26 articles.

1. D. Betten, 4-dimensionale Translationsebenen mit kommutativer Standgruppe. Math. Z. 154 (1977), 125–141. MR436004 Zbl 0335.50016

2. D. Betten, M. Forst, Transitive Wirkungen auf Flächen / Eflektive Lie-Algebren-Paare der Codimension 2. Mathematisches Seminar der Universität Kiel, 1977.

3. D. Djoković, A closure theorem for analytic subgroups of real Lie groups. Canad. Math. Bull. 19 (1976), 435–439. MR442147 Zbl 0355.22006

4. A. Förtsch, Kollineationsgruppen endlichdimensionaler topologischer Benzebenen. PhD thesis, Universität Erlangen-Nürnberg, 1982.

5. H. Groh, Topologische Laguerreebenen. I. Abh. Math. Sem. Univ. Hamburg 32 (1968), 216–231. MR234343 Zbl 0165.23603