Conics in Minkowski geometries
type: Item
instance of: scholarly article
title: Conics in Minkowski geometries
zbMATH Open document ID: 1400.51003
author: Árpád Kurusa
published in: Aequationes Mathematicae
publication date: 2018-09-26T00:00:00Z
review text: With conics defined in the usual way, the metric being that of the Minkowski geometry, as the locus of all points \(X\) whose distance to a fixed point is a constant multiple of the distance from \(X\) to a fixed hyperplane, the author proves several characterizations of Euclidean space among Minkowski geometry. Euclidean geometry is the only Minkowski geometry that has a centrally symmetric conic. Euclidean geometry is the only plane Minkowski geometry in which a quadratic conic (one which is of one of the following three types: (i) \(\{(x,y): x^2+y^2=1\}\), (ii) \(\{(x,y): x^2-y^2=1\}\), and (iii) \(\{(x,y): x=y^2\}\)) exists.
reviewed by: Victor V. Pambuccian
Mathematics Subject Classification ID: 51B20
Mathematics Subject Classification ID: 51N20
zbMATH DE Number: 6944067
zbMATH Keywords: Minkowski geometry
zbMATH Keywords: projective metric
zbMATH Keywords: centrally symmetric conic
zbMATH Keywords: quadratic conic
MaRDI profile type: Publication
full work available at URL: s00010-018-0592-1
OpenAlex ID: W2885995877
cites work: Q5822835
cites work: Q5719717
cites work: Q5445711
cites work: Conics in normed planes
cites work: Q3676766
cites work: Q3780050
Wikidata QID: Q129397070
DOI: 10.1007/S00010-018-0592-1
description: scientific article; zbMATH DE number 6944067