A Characterization of the Lüneburg Planes.
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Robert Liebler (1972)
Mathematische Zeitschrift
Andrzej Matraś (2006)
Bulletin of the Polish Academy of Sciences. Mathematics
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.
Volenec, V., Kolar-Begović, Z. (2008)
Commentationes Mathematicae Universitatis Carolinae
Adriano Barlotti (1965)
Rendiconti del Seminario Matematico della Università di Padova
František Machala (1980)
Czechoslovak Mathematical Journal
Jaroslav Lettrich (1987)
Časopis pro pěstování matematiky
Jaroslav Lettrich (1987)
Časopis pro pěstování matematiky
Kinga Cudna-Lasecka, Jan Jakóbowski (2005)
Bulletin of the Polish Academy of Sciences. Mathematics
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.
Václav Havel (1985)
Commentationes Mathematicae Universitatis Carolinae
Kinga Cudna-Salmanowicz, Jan Jakóbowski (2007)
Bulletin of the Polish Academy of Sciences. Mathematics
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.
Vladimír Volenec (1990)
Časopis pro pěstování matematiky
Jaroslava Jachanová (1988)
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica
Maier, Peter (2001)
Journal of Lie Theory
Jaroslav Lettrich, Ján Perenčaj (1988)
Časopis pro pěstování matematiky
Heinz-Richard Halder (1979)
Journal für die reine und angewandte Mathematik
Jan Jakóbowski (2005)
Bulletin of the Polish Academy of Sciences. Mathematics
There are three kinds of Benz planes: Möbius 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.
Mauro Biliotti, Armin Herzer (1982)
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
We give some examples of André-structures admitting translation groups which are transitive on the set of points but which are not normal in the dilatation group. André structures with this property seem to be new in the literature.
Johnson, Norman L. (1995)
Bulletin of the Belgian Mathematical Society - Simon Stevin
Jaroslav Lettrich (1993)
Mathematica Slovaca
Ralph-Hardo Schulz (1984)
Journal für die reine und angewandte Mathematik
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