The double tangency symmetries in Laguerre planes

• Autorzy: Kosiorek J. , Matraś A.
• Języki publikacji: EN

Abstrakty

EN

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(Y, R) following Benz.

Słowa kluczowe

EN

miquelian Laguerre plane; double tangency symmetry; projective automorphism

• Wydawca: Instytut Matematyczny PAN
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2007
• Tom: Vol. 55, no 2
• Strony: 123--137
• Opis fizyczny: Bibliogr. 12 poz.

Twórcy

autor

Kosiorek J.

autor

Matraś A.

• Department of Mathematics and Informatics, UWM Olsztyn, Żołnierska 14, 10-561 Olsztyn,

Bibliografia

• [1] R. Artzy, A symmetry theorem for Laguerre planes, J. Geom. 5 1974), 109-116.
• [2] W. Benz, Vorlesungen über Geometric der Algebren, Springer, Berlin, 1973.
• [3] E. Hartman, Transitivitatssatze fur Laguerre-Ebenen, J. Geom. 18 (1982), 9-27.
• [4] H. Groh, Laguerre planes generated by Möbius planes, Abh. Math. Sem. Hamburg 40 (1974), 43-63.
• [5] —, Flat Möbius and Laguerre planes, ibid., 64-76.
• [6] H. Karzel and H.-J. Kroll, Perspectivities in circle geometries, in: geometry—von Staudt's Point of View, P. Plaumann et al., (eds.), Proc. NATO Adv. Study Inst.(Bad Windsheim, 1980), Reidel, Dordrecht, 1981, 51-99.
• [7] J. Kosiorek and A. Matras, The symmetry axioms in Laguerre planes, Results Math. 48 (2005), 237-245.
• [8] H. Makowiecka and A. Matras, Central automorphisms of Laguerre planes, Demonstratio Math. 31 (1988), 753-763.
• [9] H. Maurer, Laguerre- und Blaschke-Modell der ebenen Laguerre-Geometric, Math. Ann. 164 (1966), 124-132.
• [10] —, Ein spiegelungsgeometrischer Aufbau der Laguerre-Geometric. I, Math. Z. 87(1965), 78-100.
• [11] —, Ein spiegelungsgeometrischer Aufbau der Laguerre-Geometric. II, ibid., 263-282.
• [12] H. Zeitler, On reflections in Minkowski planes, in: Lecture Notes in Math. 792,Springer, 1980, 183-201. 48 (2005), 237-245.