Explicit constructions of J_2-holomorphic twistor lifts

Preprint number: CP3-Origins-2011-19 and DIAS-2011-5
Authors: Martin Svensson (CP3-Origins) and John C. Wood (University of Leeds)
External link: arXiv.org

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We construct J2-holomorphic twistor lifts of all nilconformal harmonic maps from a Riemann surface into real, complex and quaternionic Grassmannians, and into the symmetric spaces SO(2m)/U(m) and Sp(m)/U(m). 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 all maps into the relevant twistor spaces which are holomorphic with respect to their non-integrable almost complex structures J2.