The energy of Hopf vector fields
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.
scientific article; zbMATH DE number 1406358