The energy of Hopf vector fields

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Abstract

The 3-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; indeed, 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.

Original languageEnglish
Pages (from-to)71-88
Number of pages18
JournalManuscripta Mathematica
Volume101
Issue number1
Publication statusPublished - Jan 2000

Keywords

  • HARMONIC MAPPINGS
  • SPHERES
  • VOLUMES
  • MAPS

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