Universität zu Köln

Struve, Rolf and Struve, Horst (2021). Absolute isotropic geometry. J. Geom., 112 (1). BASEL: SPRINGER BASEL AG. ISSN 1420-8997

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Abstract

The term 'absolute geometry' was coined by J ' anos Bolyai to characterize the part of Euclidean geometry that does not depend on the parallel postulate. In the framework of Cayley-Klein geometries the parallel axiom characterizes three classical geometries, namely Euclidean, Galilean and Minkowskian planes. We study the part of Galilean geometry that does not depend on the parallel postulate (briefly called absolute isotropic geometry) and their models (isotropic planes). After an axiomatic foundation of absolute isotropic geometry, we develop the basic theory of isotropic planes, prove the theorem of Saccheri for the angle sum of a triangle, and construct models of the different types of planes (over fields and skew fields of characteristic not equal 2). Surprisingly, these models have counterparts in the theory of Hilbert planes. The article closes with a comparison between Hilbert planes and isotropic planes.

Item Type:	Journal Article
Creators:	Creators Email ORCID ORCID Put Code Struve, Rolf UNSPECIFIED UNSPECIFIED UNSPECIFIED Struve, Horst UNSPECIFIED UNSPECIFIED UNSPECIFIED
URN:	urn:nbn:de:hbz:38-561446
DOI:	10.1007/s00022-020-00558-z
Journal or Publication Title:	J. Geom.
Volume:	112
Number:	1
Date:	2021
Publisher:	SPRINGER BASEL AG
Place of Publication:	BASEL
ISSN:	1420-8997
Language:	English
Faculty:	Unspecified
Divisions:	Unspecified
Subjects:	no entry
Uncontrolled Keywords:	Keywords Language Mathematics Multiple languages
URI:	http://kups.ub.uni-koeln.de/id/eprint/56144