On Fenchel's problem
type: Item
instance of: scholarly article
title: On Fenchel's problem
zbMATH Open document ID: 0868.53002
DOI: 10.1007/BF02274663
published in: Mathematical Notes
publication date: 1996-01-08T00:00:00Z
review text: The author considers the problem to find a criterion for the closedness of a curve of length \(\omega\) on a unit sphere in \(E^3\) by its geodesic curvature \(k(t)\) as a function of the natural parameter \(t\). This problem is related to Fenchel's problem of constructing criteria for the closedness of a space curve by given curvature and torsion as functions of the natural parameter. In this context the author proves two theorems and confirms the opinion that it is impossible to solve Fenchel's problem effectively.
Mathematics Subject Classification ID: 53A04
zbMATH DE Number: 830755
zbMATH Keywords: Fenchel's problem
zbMATH Keywords: closedness of a space curve
author: Y. Nikolayevsky
reviewed by: Stylianos Stamatakis
MaRDI profile type: Publication
cites work: On the differential geometry of closed space curves
cites work: A Differential-Geometric Criterion for a Space Curve to be Closed
full work available at URL: https://doi.org/10.1007/bf02274663
OpenAlex ID: W2094747879
description: scientific article; zbMATH DE number 830755