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New constructions of twistor lifts for harmonic maps

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Abstract

We show that given a harmonic map φ from a Riemann surface to a classical compact simply connected inner symmetric space, there is a J 2-holomorphic twistor lift of φ (or its negative) if and only if it is nilconformal. In the case of harmonic maps of finite uniton number, we give algebraic formulae in terms of holomorphic data which describes their extended solutions. In particular, this gives explicit formulae for the twistor lifts of all harmonic maps of finite uniton number from a surface to the above symmetric spaces.

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Authors and Affiliations

  1. Department of Mathematics and Computer Science, CP3–Origins Centre of Excellence for Particle Physics and Phenomenology, University of Southern Denmark, Campusvej 55, 5230, Odense M, Denmark

    Martin Svensson

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

    John C. Wood

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  1. Martin Svensson
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  2. John C. Wood
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Correspondence to Martin Svensson.

Additional information

The first author was supported by the Danish Council for Independent Research under the project Symmetry Techniques in Differential Geometry. The second author thanks the Department of Mathematics and Computer Science of the University of Southern Denmark, Odense, for support and hospitality during part of the preparation of this work.

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Svensson, M., Wood, J.C. New constructions of twistor lifts for harmonic maps. manuscripta math. 144, 457–502 (2014). https://doi.org/10.1007/s00229-014-0659-9

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  • DOI: https://doi.org/10.1007/s00229-014-0659-9

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