Abstract
A consequence of BENZ [3], [4] and ARTZY [2] is that the class of all (B *2 S2)-geometries coinzides with the class of the chain geometries σ (K,K×K), K a commutative field. Therefore the tangency theorem holds in every (B *2 S2)-geometry.
In this paper we present a corresponding tangency theorem for (B *3 G3S3)-geometries and prove that up to isomorphisms the (B *n GnSn)-geometries, n>1, are exactly the chain geometries σ (K,Kn).
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Literatur
ARTZY, R.: A Pascal Theorem Applied to Minkowski Geometry. Journal of Geometry 3 (1973), 93–102
ARTZY, R.: Addendum to A Pascal Theorem Applied to Minkowski Geometry. Journal of Geometry 3 (1973), 103–105
BENZ, W.: Vorlesungen über Geometrie der Algebren, Berlin - Heidelberg - New York 1973
BENZ, W.: Permutations and Plane Sections of a Ruled Quadric. Symposia Mathematica 5 (1971), 325–339
BENZ, W., LEISSNER, W., SCHAEFFER, H.: Kreise, Zykel, Ketten. Zur Geometrie der Algebren. Ein Bericht. Jahresbericht der Deutschen Mathematiker Vereinigung 74 (1972), 107–122
HEISE, W., KARZEL, H.: Symmetrische Minkowski Ebenen. Journal of Geometry 3 (1973), 5–20
SAMAGA, H-J.: über nichtebene Miquelsche Kurvensysteme. Dissertation Hamburg 1976
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Samaga, HJ. (B *n GnSn) — Geometrien. J Geom 12, 69–87 (1979). https://doi.org/10.1007/BF01920234
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01920234