Unit vector fields on spheres, which are harmonic maps (Q1377064)

The authors show that the Hopf vector fields on the spheres \(S^{2n+1}\) are harmonic maps from the sphere into the unit tangent bundle \(US^{2n+1}\) with the Sasaki metric. For the special case of the three-dimensional unit round sphere it is shown that the Hopf vector field is the only harmonic map into the unit tangent bundle.