Harmonic maps into the exceptional symmetric space G_2/SO(4)

Preprint number: CP3-Origins-2013-11 DNRF90 and DIAS-2013-11
Authors: Martin Svensson (IMADA) and John C. Wood (University of Leeds)
External link: arXiv.org

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We show that a harmonic map from a Riemann surface into the exceptional symmetric space G2/SO(4) has a J2-holomorphic twistor lift into one of the three flag manifolds of G2 if and only if it is `nilconformal’, i.e., has nilpotent derivative. The class of nilconformal maps includes those of finite uniton number studied by N. Correia and R. Pacheco, however we exhibit examples which are not of finite uniton number. Then we find relationships with almost complex maps from a surface into the 6-sphere; this enables us to construct examples of nilconformal harmonic maps into G2/SO(4) which are not of finite uniton number, and which have lifts into any of the three twistor spaces.