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 language | English |
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Pages (from-to) | 71-88 |
Number of pages | 18 |
Journal | Manuscripta Mathematica |
Volume | 101 |
Issue number | 1 |
Publication status | Published - Jan 2000 |
Keywords
- HARMONIC MAPPINGS
- SPHERES
- VOLUMES
- MAPS