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.
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Received: 17 March 1999
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Wood, C. The energy of Hopf vector fields. manuscripta math. 101, 71–88 (2000). https://doi.org/10.1007/s002290050005
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DOI: https://doi.org/10.1007/s002290050005