The energy of unit vector fields on the 3-sphere

The stability of the three-dimensional Hopf vector field, as a harmonic sec tion of the unit tangent bundle is viewed from a number of different angles . The spectrum of the vertical Jacobi operator is computed, and compared wi th that of the Jacobi operator of the identity map on the 3-sphere. The var iational behaviour of the three-dimensional Hopf vector field is compared a nd contrasted with that of the closely related Hopf map. Finally, it is sho wn chat the Hopf vector fields are the unique global minima of the energy f unctional restricted to unit vector fields on the 3-sphere. (C) 2001 Elsevi er Science B.V. All rights reserved. MSG: 53C20; 53C15; 58E15; 58E20.