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The Quarterly Journal of Mathematics Advance Access published online on July 10, 2008
The Quarterly Journal of Mathematics, doi:10.1093/qmath/han019
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© 2008. Published by Oxford University Press. All rights reserved. For permissions, please email: journals.permissions@oxfordjournals.org

TWISTOR SPACES, PLURIHARMONIC MAPS AND HARMONIC MORPHISMS

Bruno Ascenso Simões{dagger}

Department of Pure Mathematics, University of Leeds, Leeds LS2 9JT, UK

Martin Svensson {ddagger}

Department of Mathematics and Computer Science, University of Southern Denmark, Campusvej 55, DK-5230 Odense M, Denmark

{dagger} Corresponding author. E-mail: b.simoes{at}ptmat.fc.ul.pt

Received 2 October 2007; revised 28 May 2008
  Abstract

The application of twistor methods to construct harmonic morphisms has proved to be a fruitful approach in the 4-dimensional case, where a variety of examples and, in some cases, even a complete classification of harmonic morphisms have been found. In this paper, we generalize this construction to obtain higher-dimensional analogues of these maps. We also prove several results on twistor lifts of pluriharmonic and (1, 1)-geodesic maps.

{ddagger} E-mail: svensson{at}imada.sdu.dk


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