Abstract
The theory of Minkowski-planes has been initiated by W.Benz as an abstraction of the geometry of plane sections of a non degenerated ruled quadric in three-dimensional projective space. We give some basic definitions and concepts of this theory, including a list of properties of circle-bundles in symmetric Minkowski-planes. Finite Minkowski planes of even order are symmetric.
Minkowski-planes may be interpreted as the geometries of sharply triply sets of permutations. The most important properties of Minkowski-planes are expressed in terms of these permutation sets. In § 6 some facts on ovoidal Minkowski-planes are discussed.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Literatur
BENZ,W.: Permutations and plane sections of a ruled quadric. Symposia Mathematica 1971.
KARZEL,H.: Zusammenhänge zwischen Fastbereichen, scharf zweifach transitiven Permutationsgruppen und 2-Strukturen mit Rechtecksaxiom. Abh.Math.Sem.Univ.Hamburg32 191–206 (1968).
QVIST,B.: Some remarks concerning curves of the second degree in a finite plane. Ann. Acad.Scient.Fennicae. Series A. I.Mathem.-Phys.134 (1952).
SOPPA,R.: Scharf dreifach transitive Permutationsgruppen. Staatsexamensarbeit Hamburg 1969.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Heise, W., Karzel, H. Symmetrische Minkowski-Ebenen. J Geom 3, 5–20 (1973). https://doi.org/10.1007/BF01949702
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01949702