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Harmonic vector fields on space forms

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JournalGeometriae Dedicata
DateE-pub ahead of print - 23 Jul 2014
DatePublished (current) - 2015
Issue number1
Volume177
Number of pages29
Pages (from-to)323-352
Early online date23/07/14
Original languageEnglish

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.

    Research areas

  • Harmonic section, generalised Cheeger-Gromoll metric, conformal gradient field, Killing field, loxodromic field, dipole, conformal field, quadratic gradient field

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