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.
Original language | English |
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Pages (from-to) | 323-352 |
Number of pages | 29 |
Journal | Geometriae Dedicata |
Volume | 177 |
Issue number | 1 |
Early online date | 23 Jul 2014 |
DOIs | |
Publication status | Published - 2015 |
Keywords
- Harmonic section, generalised Cheeger-Gromoll metric, conformal gradient field, Killing field, loxodromic field, dipole, conformal field, quadratic gradient field