Harmonicity of sections of sphere bundles

We consider the energy functional on the space of sections of a sphere bundle over a Riemannian manifold equipped with the Sasaki metric and discuss the characterising condition for critical points. Furthermore, we provide a useful method for computing the tension field in some particular situations. Such a method is shown to be adequate for many tensor fields defined on manifolds M equipped with a G-structure compatible with . This leads to the construction of several new examples of differential forms which are harmonic sections or determine a harmonic map from into its sphere bundle.