Abstract
The theory of harmonic vector fields on Riemannian manifolds is generalised to pseudo-Riemannian manifolds. The congruence structure of conformal gradient fields on pseudo-Riemannian hyperquadrics and Killing fields on pseudo-Riemannian quadrics is elucidated, and harmonic vector fields of these two types are classified up to congruence. A para-Kähler twisted anti-isometry is used to correlate harmonic vector fields on the quadrics of neutral signature.
| Original language | English |
|---|---|
| Pages (from-to) | 45-58 |
| Number of pages | 14 |
| Journal | Journal of Geometry and Physics |
| Volume | 112 |
| Early online date | 27 Oct 2016 |
| DOIs | |
| Publication status | Published - Feb 2017 |
Bibliographical note
© 2016 Elsevier B.V. All rights reserved. This is an author-produced version of the published paper. Uploaded in accordance with the publisher’s self-archiving policy.Keywords
- Harmonic map, harmonic section, pseudo-Riemannian vector bundle, generalised Cheeger-Gromoll metric, pseudo-Riemannian manifold, pseudo-Riemannian space form, Killing field, conformal gradient field, anti-isometry, para-Kaehler structure
- Anti-isometry
- Conformal gradient field
- Generalised Cheeger–Gromoll metric
- Harmonic section
- Killing field
- Pseudo-Riemannian vector bundle
