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Unit vector fields on spheres, which are harmonic maps. (English) Zbl 0891.53024
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.

##### MSC:
 53C20 Global Riemannian geometry, including pinching 58E20 Harmonic maps, etc.
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