Some generalization of nearaffine planes

• Autorzy: Jakóbowski J.

Identyfikatory

DOI

10.4064/ba53-1-8

• Języki publikacji: EN

Abstrakty

EN

There are three kinds of Benz planes: Mobius planes, Laguerre planes and Minkowski planes. A Minkowski plane satisfying an additional axiom is connected with some other structure called a nearaffine plane. We construct an analogous structure for a Laguerre plane. Moreover, our description is common for both cases.

Słowa kluczowe

EN

affine plane; external structure; Laguerre plane; Minkowski plane; nearaffine plane

PL

płaszczyzna afiniczna; struktura zewnętrzna; płaszczyzna Laguerre'a; płaszczyzna Minkowskiego

• Wydawca: Instytut Matematyczny PAN
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2005
• Tom: Vol. 53, no 1
• Strony: 87--97
• Opis fizyczny: Bibliogr. 11 poz.

Twórcy

autor

Jakóbowski J.

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

Bibliografia

• [1] J. André, Some new results on incidence structures, in: Colloquio Internazionale sulle Teorie Combinatori, Vol. II, Atti dei Convegni Lincei 17, 1976, 201–222.
• [2] W. Benz, Vorlesungen über Geometrie der Algebren, Springer, Berlin, 1973.
• [3] Y. Chen, A characterization of some geometries of chains, Canad. J. Math. 26 (1974), 257–272.
• [4] P. Dembowski, Finite Geometries, Springer, Berlin, 1968.
• [5] W. Heise und H. Seybold, Das Existenzproblem der Möbius-, Laguerre- und Minkowski-Erweiterungen endlicher affiner Ebenen, Sitz. Ber. Bayer. Akad. Wiss. Math.-Nat. Kl. 1975, 43–58.
• [6] J. Jakóbowski, Nearaffine planes related to pseudo-ordered fields, Bull. Polish Acad. Sci. Math. 50 (2002), 345–360.
• [7] H. J. Kroll, Anordnungsfragen in Benz-Ebenen, Abh. Math. Semin. Univ. Hamburg 46 (1977), 217–255.
• [8] R. Löwen and R. U. Pfüller, Two-dimensional Laguerre planes over convex functions, Geom. Dedicata 23 (1987), 73–85.
• [9] N. Percsy, Finite Minkowski planes in which every circle-symmetry is an automorphism, ibid. 10 (1981), 269–282.
• [10] H. A. Wilbrink, Finite Minkowski planes, Geom. Dedicata 12 (1982), 119–129.
• [11] —, Nearaffine planes, ibid. 12 (1982), 53–62.