Harmonicity of sections of sphere bundles

SALVAI, MARCOS; GONZÁLEZ DÁVILA, J C; MARTIN CABRERA, F

MATHEMATISCHE ZEITSCHRIFT

Año: 2007 p. 1 - 1

0025-5874

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 formany tensor fields defined on manifolds M equipped with a G-structure compatible with the Riemannian structure. This leads to the construction of several new examples of differential forms which are harmonic sections or determine a harmonic map from M into its sphere bundle.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 formany tensor fields defined on manifolds M equipped with a G-structure compatible with the Riemannian structure. This leads to the construction of several new examples of differential forms which are harmonic sections or determine a harmonic map from M into its sphere bundle.