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Manuscripta Mathematica

, Volume 144, Issue 3–4, pp 457–502 | Cite as

New constructions of twistor lifts for harmonic maps

  • Martin SvenssonEmail author
  • John C. Wood
Article

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.

Mathematics Subject Classification (2000)

53C43 58E20 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.Department of Mathematics and Computer Science, CP3–Origins Centre of Excellence for Particle Physics and PhenomenologyUniversity of Southern DenmarkOdense MDenmark
  2. 2.Department of Pure MathematicsUniversity of LeedsLeedsUK

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