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 M(𝔽,ℝ) of automorphisms of a chain geometry Σ(𝔽,ℝ) following Benz.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ba55-2-3,
author = {Jaros\l aw Kosiorek and Andrzej Matra\'s},
title = {The Double Tangency Symmetries in Laguerre Plane},
journal = {Bulletin of the Polish Academy of Sciences. Mathematics},
volume = {55},
year = {2007},
pages = {123-137},
zbl = {1124.51002},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ba55-2-3}
}
Jarosław Kosiorek; Andrzej Matraś. The Double Tangency Symmetries in Laguerre Plane. Bulletin of the Polish Academy of Sciences. Mathematics, Tome 55 (2007) pp. 123-137. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ba55-2-3/