The Double Tangency Symmetries in Laguerre Plane
Tom 55 / 2007
Bulletin Polish Acad. Sci. Math. 55 (2007), 123-137
MSC: Primary 51B15.
DOI: 10.4064/ba55-2-3
Streszczenie
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.
