The energy of Hopf vector fields |
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Authors: | C M Wood |
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Institution: | (1) Department of Mathematics, University of York, Heslington, York Y01 5DD, UK. E-mail: cmw4@york.ac.uk, GB |
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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.
Received: 17 March 1999 |
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Keywords: | Mathematics Subject Classification (1991):53C20 (53C15 58E15 58E20) |
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