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On the geometry of harmonic morphisms

Published online by Cambridge University Press:  24 October 2008

Sigmundur Gudmundsson
Sigmundur Gudmundsson
Affiliation:
Department of Pure Mathematics, University of Leeds, Leeds LS2 9JT
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Abstract

Let π:M→B be a horizontally conformal submersion. We give necessary curvature conditions on the manifolds M and B, which lead to non-existence results for certain horizontally conformal maps, and harmonic morphisms. We then classify all such maps between open subsets of Euclidean spaces, which additionally have totally geodesic fibres and are horizontally homothetic. They are orthogonal projections on each connected component, followed by a homothety.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 108 , Issue 3 , November 1990 , pp. 461 - 466
Copyright
Copyright © Cambridge Philosophical Society 1990

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