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Harmonic vector fields on space forms
Research output: Contribution to journal › Article › peer-review
Links
- http://maths.york.ac.uk/www/sites/default/files/Preprint_No 03_2012_2013.pdf
- http://arxiv.org/abs/1301.6075
Published copy (DOI)
Author(s)
Department/unit(s)
Publication details
| Journal | Geometriae Dedicata |
|---|---|
| Date | E-pub ahead of print - 23 Jul 2014 |
| Date | Published (current) - 2015 |
| Issue number | 1 |
| Volume | 177 |
| Number of pages | 29 |
| Pages (from-to) | 323-352 |
| Early online date | 23/07/14 |
| Original language | English |
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.
- Harmonic section, generalised Cheeger-Gromoll metric, conformal gradient field, Killing field, loxodromic field, dipole, conformal field, quadratic gradient field
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