Polar curves in the non-Euclidean geometry
type: Item
instance of: scholarly article
title: Polar curves in the non-Euclidean geometry
zbMATH Open document ID: 1148.53010
published in: Results in Mathematics
publication date: 2008-09-04T00:00:00Z
review text: The author studies the geometry of polar closed convex curves in the spherical and in the hyperbolic plane (in the last case, the curves are also supposed horocyclic) by means of a representation of these curves by suitable support functions. He proves the following: (1) The differential quotients of the arclengths of a curve \(C\) and the polar curve \(C^*\) coincide with the curvature of \(C\). (2) The (suitably defined) curvature of \(C^*\) is inverse to the curvature of \(C\). The author notes that these properties are simpler than the corresponding properties in Euclidean geometry. He also notes that the evolute of a convex curve can be represented by support functions in a simple manner.
reviewed by: Athanase Papadopoulos
Mathematics Subject Classification ID: 53A35
Mathematics Subject Classification ID: 52A55
zbMATH DE Number: 5320909
zbMATH Keywords: polar convex curve
zbMATH Keywords: support function of spherical convex curve
zbMATH Keywords: support function of horocyclic convex curve
zbMATH Keywords: non-Euclidean evolute
author: Kurt Leichtweiß
MaRDI profile type: Publication
full work available at URL: s00025-007-0247-3
OpenAlex ID: W2140887599
DOI: 10.1007/S00025-007-0247-3
description: scientific article; zbMATH DE number 5320909