Harmonic Vector Fields on Space Forms
Abstract
A vector field s on a Riemannian manifold M is said to be harmonic if there exists a member of a 2-parameter family of generalised Cheeger-Gromoll metrics on TM with respect to which s is a harmonic section. If M is a simply-connected non-flat space form other than the 2-sphere, examples are obtained of conformal vector fields that are harmonic. In particular, the harmonic Killing fields and conformal gradient fields are classified, a loop of non-congruent harmonic conformal fields on the hyperbolic plane constructed, and the 2-dimensional classification achieved for conformal fields. A classification is then given of all harmonic quadratic gradient fields on spheres.
Keywords
Cite
@article{arxiv.1301.6075,
title = {Harmonic Vector Fields on Space Forms},
author = {M. Benyounes and E. Loubeau and C. M. Wood},
journal= {arXiv preprint arXiv:1301.6075},
year = {2013}
}
Comments
29 pages. This is such a complete overhaul of arXiv:math/0703060 that we submit it as new article