Binormal motion of curves with constant torsion in 3-spaces
type: Item
instance of: scholarly article
title: Binormal motion of curves with constant torsion in 3-spaces
zbMATH Open document ID: 1403.53054
DOI: 10.1155/2017/7075831
author: Josu Arroyo
author: Oscar J. Garay
author: Álvaro Pámpano
published in: Advances in Mathematical Physics
publication date: 2018-10-23T00:00:00Z
review text: The authors use a geometrical approach to investigate an extension of the localized induction equation \(x_{t}=x_{s}\times x_{ss}\) which is a soliton equation. Under some suitable conditions a curve motion describes a curve \(\gamma\) evolving under the binormal flow, determines an immersed surface \(S_{\gamma}\) in a Riemannian or Lorentzian 3-space with constant curvature. Applying fundamental results of theory of submaifolds, they obtain the curvature and torsion of a geodesic foliation of \(S_{\gamma}\). Also, they study the binormal evolution surfaces, whose filaments have the same constant torsion and use the Gauss-Codazzi equations to construct solutions.
reviewed by: Ergin Bayram
Mathematics Subject Classification ID: 53C44
Mathematics Subject Classification ID: 53A04
Mathematics Subject Classification ID: 53A05
Mathematics Subject Classification ID: 35K60
zbMATH DE Number: 6962661
zbMATH Keywords: binormal flow
zbMATH Keywords: Gauss-Codazzi equations
zbMATH Keywords: soliton solution
zbMATH Keywords: contant torsion
Wikidata QID: Q59142464
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2017/7075831
OpenAlex ID: W2732878908
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description: scientific article; zbMATH DE number 6962661