A construction of a skewaffine structure in Laguerre geometry

• Autorzy: Matraś A.
• Języki publikacji: EN

Abstrakty

EN

J. Andre constructed a skewaffine structure as a group space of a normally transitive group. In this paper his construction is used to describe the structure of the set of circles not passing through a point of a Laguerre plane. Sufficient conditions to ensure that this structure is a skewaffine plane are given.

Słowa kluczowe

EN

miquelian Laguerre plane; symetry axiom

• Wydawca: Instytut Matematyczny PAN
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2006
• Tom: Vol. 54, no 3-4
• Strony: 277--289
• Opis fizyczny: Bibliogr. 12 poz.

Twórcy

autor

Matraś A.

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

Bibliografia

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• [4] Y. Chen, A characterization of some geometries of chains, Canad. J. Math. 26 (1974), 257-272.
• [5] K. Griming, Kegelschnitte und steinersche Ovale in Fano-Ebenen, Arch. Math. (Basel) 49 (1987), 459-464.
• [6] E. Hartman, Transitivitatssatze fiir Laguerre-Ebenen, J. Georn. 18 (1982), 9-27.
• [7] D. Hughes and F. Piper, Projective Planes, Springer, 1970.
• [8] R. Kleinewillinghofer, Eine Klassifikation der Laguerre-Ebenen nach L-Streckungen und L-Translationen, Arch. Math. (Basel) 34 (1980), 469-480.
• [9] H. Makowiecka and A. Matras, Central automorphisms of Laguerre planes, Demonstratio Math. 31 (1998), 753-763.
• [10] J. Pfalzgraf, Über ein Modell für nichtkommutative geometrische Räume, Dissertation, Saarbrücken 1984.
• [11] A. Schroth, Topological Circle Planes and Topological Quadrangles, Longman, 1995.
• [12] H. A. Wilbrink, Nearaffine planes and Minkowski planes, Master's Thesis, Eindhoven Univ. of Technology, 1978.