The energy of unit vector fields on the 3-sphere
Differential Geometry
2009-10-31 v1
Abstract
The stability of the 3-dimensional Hopf vector field, as a harmonic section of the unit tangent bundle, is viewed from a number of different angles. The spectrum of the vertical Jacobi operator is computed, and compared with that of the Jacobi operator of the identity map on the 3-sphere. The variational behaviour of the 3-dimensional Hopf vector field is compared and contrasted with that of the closely-related Hopf map. Finally, it is shown that the Hopf vector fields are the unique global minima of the energy functional restricted to unit vector fields on the 3-sphere.
Keywords
Cite
@article{arxiv.math/0005293,
title = {The energy of unit vector fields on the 3-sphere},
author = {A. Higuchi and B. S. Kay and C. M. Wood},
journal= {arXiv preprint arXiv:math/0005293},
year = {2009}
}
Comments
AMSTeX, 20 pages, to appear in J Geom Phys