A rough classification of symmetric planes.
Löwe, Harald (2001)
Advances in Geometry
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Löwe, Harald (2001)
Advances in Geometry
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Johnson, N.L. (1989)
International Journal of Mathematics and Mathematical Sciences
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Sam B. Nadler, Jr. (1977)
Colloquium Mathematicae
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Jan Jakóbowski (2005)
Bulletin of the Polish Academy of Sciences. Mathematics
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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.
Salzmann, H. (2003)
Advances in Geometry
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Johnson, N.L. (1981)
International Journal of Mathematics and Mathematical Sciences
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Kinga Cudna-Salmanowicz, Jan Jakóbowski (2007)
Bulletin of the Polish Academy of Sciences. Mathematics
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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.
Jha, V., Johnson, N. L. (2003)
Advances in Geometry
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Johnson, N.L. (1982)
International Journal of Mathematics and Mathematical Sciences
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Metsch, K. (2003)
Advances in Geometry
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Johnson, N.L. (1978)
International Journal of Mathematics and Mathematical Sciences
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Günter Steinke (1983)
Mathematische Zeitschrift
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Hiramine, Yutaka, Jha, Vikram, Johnson, Norman L. (2001)
International Journal of Mathematics and Mathematical Sciences
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Foulser, D.A., Johnson, N.L., Ostrom, T.G. (1983)
International Journal of Mathematics and Mathematical Sciences
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Quaisser, Erhard (1998)
Beiträge zur Algebra und Geometrie
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