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Laguerre and Minkowski planes with neighbor relation

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Abstract

In [7] we have introduced the notion of a Möbius plane with neighbor relation as a generalization of ordinary Möbius planes. In this paper we present two other classes of circle geometries which are locally affine Klingenberg planes: Laguerre and Minkowski planes with neighbor relation.

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References

  1. ARTMANN, B., DORN, G., DRAKE, D.A., TÖRNER, G.: Hjelmslevsche Inzidenzgeometrie und verwandte Gebiete, Literaturverzeichnis. J.Geom. 7 (1976), 175–191

    Google Scholar 

  2. BENZ, W.: Vorlesungen über Geometrie der Algebren. Springer, Berlin-Heidelberg-New York 1973

    Google Scholar 

  3. DEMBOWSKI, P.: Finite Geometries. Springer, Berlin-Heidelberg -New York 1968

    Google Scholar 

  4. HJELMSLEV, J.: Die Geometrie der Wirklichkeit. Acta Math. 40 (1916), 33–66

    Google Scholar 

  5. HJELMSLEV, J.: Die natürliche Geometrie. Abh.Math.Sem.Univ. Hamburg 2 (1923), 1–36

    Google Scholar 

  6. JUNGNICKEL, D.: Hjelmslevsche Inzidenzgeometrie und verwandte Gebiete, Literaturverzeichnis II. J.Geom. 16 (1981), 138–147

    Google Scholar 

  7. KEPPENS, D.: Möbius planes with neighbor relation. to appear in Simon Stevin

  8. KLEINFELD, E.: Finite Hjelmslev planes. Illinois J.Math. 3 (1959), 403–407

    Google Scholar 

  9. KLINGENBERG, W.: Projektive und affine Ebenen mit Nachbarelementen. Math.Z. 60 (1954), 384–406

    Google Scholar 

  10. KLINGENBERG, W.: Desarguessche Ebenen mit Nachbarelementen. Abh.Math.Sem.Univ.Hamburg 20 (1955), 97–111

    Google Scholar 

  11. LANE, N.D. & LORIMER, J.W.: Desarguesian affine Hjelmslev Planes. J.Reine Angew.Math. 278/279 (1975), 336–352

    Google Scholar 

  12. LANG, K.: Spiegelungen in Hjelmslevschen Kreisgeometrien. Geom.Ded. 21 (1986), 107–121

    Google Scholar 

  13. LANG, K.: Kreisgeometrien mit Nachbarelementen. Submitted

  14. LÜNEBURG. H.: Affine Hjelmslev-Ebenen mit transitiver Translationsgruppe. Math.Z.79 (1962), 260–288

    Google Scholar 

  15. PERCSY, N.: Finite Minkowski planes in which every circle-symmetry is an automorphism. Geom.Ded. 5 (1981), 269–282

    Google Scholar 

  16. SEIER, W.: Kettengeometrie über Hjelmslevringen, Beiträge zur geometrischen Algebra, Proceedings Duisburg 1976, Birkhäuser

  17. Van MALDEGHEM, H.: Incidence geometries related to rank 3 affine buildings, to appear in Proceedings of Combinatorics '86, Mendola 1986

  18. WILLEMS, M.: Een meetkundige en kombinatorische Studie van Benzstrukturen, thesis 1984

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Research supported by IWONL grant no-840037

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Keppens, D. Laguerre and Minkowski planes with neighbor relation. J Geom 30, 12–27 (1987). https://doi.org/10.1007/BF01223259

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  • DOI: https://doi.org/10.1007/BF01223259

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