The energy of Hopf vector fields
type: Item
instance of: scholarly article
title: The energy of Hopf vector fields
zbMATH Open document ID: 0946.53032
published in: Manuscripta Mathematica
publication date: 2000-10-17T00:00:00Z
review text: The three-dimensional Hopf vector field is shown to be a stable harmonic section of the unit tangent bundle. In contrast, higher-dimensional Hopf vector fields are unstable harmonic sections; there is a natural variation through smooth unit vector fields which is locally energy-decreasing, and whose asymptotic limit is a singular vector field of finite energy. This energy is explicitly calculated, and conjectured to be the infimum of the energy functional over all smooth unit vector fields.
reviewed by: Marian Ioan Munteanu
Mathematics Subject Classification ID: 53C43
Mathematics Subject Classification ID: 58E20
zbMATH DE Number: 1406358
zbMATH Keywords: Hopf vector field
zbMATH Keywords: harmonic section
zbMATH Keywords: unit tangent bundle
zbMATH Keywords: energy functional
author: C. M. Wood
MaRDI profile type: Publication
full work available at URL: s002290050005
OpenAlex ID: W2072935629
DOI: 10.1007/S002290050005
description: scientific article; zbMATH DE number 1406358