On the curvature of circles and curves in \(\mathbb{H}^n\)
type: Item
instance of: scholarly article
zbMATH Open document ID: 0989.53005
author: Maciej Czarnecki
published in: Demonstratio Mathematica
publication date: 2001-07-12T00:00:00Z
Mathematics Subject Classification ID: 53A35
Mathematics Subject Classification ID: 53C30
zbMATH DE Number: 1619035
zbMATH Keywords: osculating circles
zbMATH Keywords: curvature of smooth curves
zbMATH Keywords: Poincaré-model
zbMATH Keywords: hyperbolic space
zbMATH Keywords: Euclidean circles
MaRDI profile type: Publication
full work available at URL: dema-2001-0120
OpenAlex ID: W1042458752
DOI: 10.1515/DEMA-2001-0120
title: On the curvature of circles and curves in \(\mathbb{H}^n\)
review text: The author computes the curvature of smooth curves in the Poincaré-model of the hyperbolic space \(\mathbb{H}^n_a\) (with constant curvature \(-a^2)\), and applies it to arcs of Euclidean circles in \(\mathbb{H}^n_ a\). Osculating circles are used to prove that any closed curve in \(\mathbb{H}^n_a\) carries at least one point, where the curvature is greater than \(a\).
reviewed by: Friedrich Manhart
description: scientific article; zbMATH DE number 1619035