Multicentral automorphisms in geometries of circles

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

Abstrakty

EN

We consider three types of geometries of circles (Moebius plane, Laguerre plane and Minkowski plane, cf. [4) with respect to so-called multicentral automorphisms. An automorphism [phi] of any geometry of circles is central if it has a fix point P and [phi] becomes a central collineation in the derived projective plane M(P). For any central automorphism [phi] we try to establish the whole set of points R such that [phi] becomes a central collineation in M(R.). Than [phi] is called multicentral if this set contains at least two points. Moreover, [phi] is proper if existing of a point [R is not equal to P], is not caused by the fact that [phi] is central in M(P). There is no proper multicentral automorphism in a Moebius plane. The most interesting proper multicentral automorphisms are involutorial mappings: double homotheties in Minkowski planes, and (sigma, tau)homologies in Laguerre planes. We give some examples.

Słowa kluczowe

EN

central automorphism; homothety; Laguerre planes; Minkowski planes; Moebius planes; translation

PL

automorfizm centralny; jednokładność; płaszczyzna Laguerre'a; płaszczyzna Minkowskiego; płaszczyzna Moebiusa; translacja

• Wydawca: Instytut Matematyczny PAN
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2001
• Tom: Vol. 49, no 4
• Strony: 417--432
• Opis fizyczny: Bibliogr. 14 poz.,

Twórcy

autor

Jakóbowski J.

autor

Matraś A.

• Faculty of Mathematics and Informatics, University of Warmia and Mazury in Olsztyn, ul. Żołnierska 14, 10-561 Olsztyn, Poland,