Extending nearaffine planes to hyperbola structures

• Autorzy: Cudna-Salmanowicz K. , Jakóbowski J.
• Języki publikacji: EN

Abstrakty

EN

H. A. Wilbrink [Geom. Dedicata 12 (1982)] considered a class of Minkowski planes whose restrictions, called residual planes, are nearaffine planes. Our study goes in the opposite direction: what conditions on a nearaffine plane are necessary and sufficient to get an extension which is a hyperbola structure.

Słowa kluczowe

EN

affine plane; Desargues postulate; hyperbola structure; nearaffine plane; Veblen condition

• Wydawca: Instytut Matematyczny PAN
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2007
• Tom: Vol. 55, no 1
• Strony: 71--80
• Opis fizyczny: Bibliogr. 7 poz., wykr.

Twórcy

autor

Cudna-Salmanowicz K.

autor

Jakóbowski J.

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

Bibliografia

• [1] J. Andre, On finite non-commutative affine spaces, in: M. Hall and J. H. von Lint (eds.), Combinatorics, Part I, Math. Centre Tracts 55, 1974, 60-107.
• [2] —, Some new results on incidence structures, in: Atti dei Convegni Lincei 17, Colloquio Internazionale sulle teorie combinatori II, 1976, 201-222.
• [3] K. Cudna-Lasecka and J. Jakóbowski, Central automorphisms of veblenian nearaffine planes, Bull. Polish Acad. Sci. Math. 53 (2005), 337-347.
• [4] J. Jakobowski, Nearaffine planes related to pseudo-ordered fields, ibid. 50 (2002), 345-360.
• [5] N. Percsy, Finite Minkowski planes in which every circle-symmetry is an automorphism, Geom. Dedicata 10 (1981), 269-282.
• [6] H. A. Wilbrink, Finite Minkowski planes, ibid. 12 (1982), 119-129.
• [7] —, Nearaffine planes, ibid. 12 (1982), 53-62.