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A FLAT LAGUERRE PLANE OF KLEINEWILLINGHÖFER TYPE V

Part of: Topological geometry

Published online by Cambridge University Press:  18 November 2011

JEROEN SCHILLEWAERT  and
GÜNTER F. STEINKE
JEROEN SCHILLEWAERT
Affiliation:
Département de Mathématique, Université Libre de Bruxelles, CP 216, Bd du Triomphe, B-1050 Bruxelles, Belgium (email: jschille@ulb.ac.be)
GÜNTER F. STEINKE*
Affiliation:
Department of Mathematics and Statistics, University of Canterbury, Private Bag 4800, Christchurch 8140, New Zealand (email: gunter.steinke@canterbury.ac.nz)
*
✉For correspondence; e-mail: gunter.steinke@canterbury.ac.nz
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Abstract

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The Kleinewillinghöfer types of Laguerre planes reflect the transitivity properties of certain groups of central automorphisms. Polster and Steinke have shown that some of the conceivable types for flat Laguerre planes cannot exist and given models for most of the other types. The existence of only a few types is still in doubt. One of these is type V.A.1, whose existence we prove here. In order to construct our model, we make systematic use of the restrictions imposed by the group. We conjecture that our example belongs to a one-parameter family of planes all of type V.A.1.

Keywords

Laguerre planeKleinewillinghöfer typetopological geometry

MSC classification

Secondary: 51H15: Topological nonlinear incidence structures
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 91 , Issue 2 , October 2011 , pp. 257 - 274
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2011

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