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The energy of Hopf vector fields

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Publication details

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

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.

    Research areas

  • HARMONIC MAPPINGS, SPHERES, VOLUMES, MAPS

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