Let (M, g) be a Riemannian manifold. When M is compact and the tangent bundle TM is equipped with the Sasaki metric gs, the only vector fields which define harmonic maps from (M, g) to (TM, gs), are the parallel ones. The Sasaki metric, and other well known Riemannian metrics on TM , are particular examples of g-natural metrics. We equip TM with an… (More)
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