Some Connections between Minkowski and Hyperbolic Planes

Volume 52 / 2004

Jarosław Kosiorek, Andrzej Matraś Bulletin Polish Acad. Sci. Math. 52 (2004), 133-139 MSC: Primary 51B20. DOI: 10.4064/ba52-2-4

Abstract

The model of the Minkowski plane in the projective plane with a fixed conic sheds a new light on the connection between the Minkowski and hyperbolic geometries. The construction of the Minkowski plane in a hyperbolic plane over a Euclidean field is given. It is also proved that the geometry in an orthogonal bundle of circles is hyperbolic in a natural way.

Authors

  • Jarosław KosiorekFaculty of Mathematics and Computer Science
    University of Warmia and Mazury
    /Zołnierska 14
    10-561 Olsztyn, Poland
  • Andrzej MatraśFaculty of Mathematics and Computer Science
    University of Warmia and Mazury
    /Zołnierska 14
    10-561 Olsztyn, Poland
    e-mail

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