Harmonicity of unit vector fields with respect to Riemannian g-natural metrics

Let (M, g) be a compact Riemannian manifold and T1M its unit tangent sphere bundle. Unit vector fields defining harmonic maps from (M, g) to (T1M, (g) over bar (s)), (g) over bar (s) being the Sasaki metric on T1M, have been extensively studied. The Sasaki metric, and other well known Riemannian metrics on T1M, are particular examples of g-natural metrics. We equip T1M with an arbitrary Riemannian g-natural metric (G) over bar, anti investigate the harmonicity of a unit vector field V of M, thought as a map from (M, g) to (T1M, (G) over bar). We then apply this study to characterize unit Killing vector fields and to investigate harmonicity properties of the Reeb vector field of a contact metric manifold. (C) 2008 Elsevier B.V. All rights reserved.