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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ba52-2-4,
author = {Jaros\l aw Kosiorek and Andrzej Matra\'s},
title = {Some Connections between Minkowski and Hyperbolic Planes},
journal = {Bulletin of the Polish Academy of Sciences. Mathematics},
volume = {52},
year = {2004},
pages = {133-139},
zbl = {1108.51005},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ba52-2-4}
}
Jarosław Kosiorek; Andrzej Matraś. Some Connections between Minkowski and Hyperbolic Planes. Bulletin of the Polish Academy of Sciences. Mathematics, Tome 52 (2004) pp. 133-139. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ba52-2-4/