Houston journal of mathematics vol:27 issue:2 pages:377-409
We consider unit vector fields on homogeneous Riemannian manifolds (M = G/G(o) g) which are G-invariant. We derive a criterion for the minimality and for the harmonicity of such vector fields by means of the infinitesimal models which correspond to (locally) homogeneous spaces and which are determined by using homogeneous structures. This leads to the construction of a lot of new examples of unit vector fields which are minimal or harmonic or which determine a harmonic map from (M, g) into its unit tangent sphere bundle equipped with the Sasaki metric. For several cases we obtain the complete list of such vector fields, in particular for low dimensions.