The Double Tangency Symmetries in Laguerre Plane

Volume 55 / 2007

Jaros/law Kosiorek, Andrzej Matraś Bulletin Polish Acad. Sci. Math. 55 (2007), 123-137 MSC: Primary 51B15. DOI: 10.4064/ba55-2-3

Abstract

The group generated by double tangency symmetries in a Laguerre plane is investigated. The geometric classification of involutions of a symmetric Laguerre plane is given. We introduce the notion of projective automorphisms using the double tangency and parallel perspectivities. We give the description of the groups of projective automorphisms and automorphisms generated by double tangency symmetries as subgroups of the group $\textbf M(\mathbb{F},\mathbb{R})$ of automorphisms of a chain geometry ${\mit\Sigma}(\mathbb{F},\mathbb{R})$ following Benz.

Authors

  • Jaros/law KosiorekDepartment of Mathematics and Informatics
    UWM Olsztyn
    Żo/lnierska 14
    10-561 Olsztyn, Poland
    e-mail
  • Andrzej MatraśDepartment of Mathematics and Informatics
    UWM Olsztyn
    Żo/lnierska 14
    10-561 Olsztyn, Poland
    e-mail

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