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arXiv · 1301.6075

Harmonic Vector Fields on Space Forms

M. Benyounes·E. Loubeau·C. M. Wood
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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.

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M. Benyounes, E. Loubeau, C. M. Wood. 2013-01-25. Harmonic Vector Fields on Space Forms. https://arxiv.org/abs/1301.6075

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