New constructions of twistor lifts for harmonic maps

Details New constructions of twistor lifts for harmonic maps New constructions of twistor lifts for harmonic maps

2011-06-09

arxiv.org/abs/1106.1832v4

Mathematics

Differential Geometry

Some minor improvements and corrections made. Title and introduction changed to reflect better the content of the paper

Scientific paper

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.

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