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4 Bulletin of the Polish Academy of Sciences. Mathematics

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Extending nearaffine planes to hyperbola structures

100%

Cudna-Salmanowicz K. , Jakóbowski J.

Bulletin of the Polish Academy of Sciences. Mathematics

2007

tom 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.

Note about the set S[f] for a polynomial mapping f : [C^2 --> C^2]

86%

Jelonek Z.

Bulletin of the Polish Academy of Sciences. Mathematics

2001

tom Vol. 49, no 1

67--72

The aim of this paper is to give a simple method of computing the set S[f] of points at which a generically-finite polynomial mapping f : [C^2 --> C^2] is not proper.

Some generalization of nearaffine planes

72%

Jakóbowski J.

Bulletin of the Polish Academy of Sciences. Mathematics

2005

tom 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

72%

Cudna-Lasecka K. , Jakóbowski J.

Bulletin of the Polish Academy of Sciences. Mathematics

2005

tom 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.