J Austral Math Soc Ser A 51 pp118--153, 1991.

Harmonic Morphisms and Conformal Foliations by Geodesics of Three-Dimensional Space Forms

Paul Baird and John C. Wood

Abstract

A complete classification is given of harmonic morphisms to a surface and conformal foliations by geodesics, with or without isolated singularities, of a simply-connected space form. The method is to associate to any such a holomorphic map from a Riemann surface into the space of geodesics of the space form. Properties such as nonintersecting fibres (or leaves) are translated into conditions on the holomorphic mapping which show it must have a simple form corresponding to a standard example.

1980 AMS Subject Classification (1985 Revision): 53C12, 58E20, 31B99

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Authors

Paul Baird

John C. Wood

Department of Pure Mathematics, University of Leeds, Leeds LS29JT, United Kingdom.