  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.
