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Harmonic characteristic vector fields on contact metric three-manifolds

Published online by Cambridge University Press:  17 April 2009

Domenico Perrone
Domenico Perrone
Affiliation:
Dipartimento di Matematica, Universitá degli Studi di Lecce, Via Provinciale Lecce-Arnesano, 73100 Lecce, Italy e-mail: demenico.perrone@unile.it
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Abstract

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In this paper we show that a contact metric three-manifold is a generalised (k, μ)-space on an everywhere dense open subset if and only if its characteristic vector field ξ determines a harmonic map from the manifold into its unit tangent sphere bundle equipped with the Sasaki metric. Moreover, we classify the contact metric three-manifolds whose characteristic vector field ξ is strongly normal (or equivalently, is harmonic and minimal).

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 67 , Issue 2 , April 2003 , pp. 305 - 315
Copyright
Copyright © Australian Mathematical Society 2003

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