# New constructions of twistor lifts for harmonic maps

Martin Svensson, John C. Wood

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## Abstrakt

We show that given a harmonic map \varphi from a Riemann surface into a classical simply connected compact inner symmetric space, there is a J_2-holomorphic twistor lift of \varphi (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.
Originalsprog Engelsk Manuscripta Mathematica 144 3-4 457-502 0025-2611 https://doi.org/10.1007/s00229-014-0659-9 Udgivet - 2014