Harmonicity of sections of sphere bundles
Differential Geometry
2007-11-26 v1
Abstract
We consider the energy functional on the space of sections of a sphere bundle over a Riemannian manifold (M, <,>) equipped with the Sasaki metric and we discuss the characterising condition for critical points. Likewise, 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 a lot of new examples of differential forms which are harmonic sections or determine a harmonic map from (M,<,>) into its sphere bundle.
Cite
@article{arxiv.0711.3703,
title = {Harmonicity of sections of sphere bundles},
author = {J. C. Gonzalez-Davila and F. Martin Cabrera and M. Salvai},
journal= {arXiv preprint arXiv:0711.3703},
year = {2007}
}
Comments
22 pages