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Harmonic vector fields on pseudo-Riemannian manifolds

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JournalJournal of Geometry and Physics
DateAccepted/In press - 18 Sep 2016
DateE-pub ahead of print - 27 Oct 2016
DatePublished (current) - Feb 2017
Volume112
Number of pages14
Pages (from-to)45-58
Early online date27/10/16
Original languageEnglish

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.

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© 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.

    Research areas

  • 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

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