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3 Bulletin of the Polish Academy of Sciences. Mathematics

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Extending nearaffine planes to hyperbola structures

Cudna-Salmanowicz K., Jakóbowski J.

Bulletin of the Polish Academy of Sciences. Mathematics

2007

Vol. 55, no 1

71-80

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.

Some generalization of nearaffine planes

Jakóbowski J.

Bulletin of the Polish Academy of Sciences. Mathematics

2005

Vol. 53, no 1

87-97

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.

Central automorphisms of Veblenian nearaffine planes

Cudna-Lasecka K., Jakóbowski J.

Bulletin of the Polish Academy of Sciences. Mathematics

2005

Vol. 53, no 3

337-347

The paper deals with nearaffine planes described by H. A. Wilbrink. We consider their central automorphisms, i.e. automorphisms satisfying the Veblen condition, which become central collineations in connected projective planes. Moreover, a concept of central pseudo-automorphism is considered, i.e. some bijections in a nearaffine plane are not automorphisms but they become central collineations in the related projective planes.