## Abstract

We show that a harmonic map from a Riemann surface into the exceptional symmetric space $G_2/{\mathrm SO}(4)$ has a $J_2$-holomorphic twistor lift into one of the three flag manifolds of $G_2$ 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 $G_2/{\mathrm SO}(4)$ which are not of finite uniton number, and which have lifts into any of the three twistor spaces.

Original language | English |
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Journal | Journal of the London Mathematical Society |

Volume | 91 |

Issue number | 1 |

Pages (from-to) | 291-319 |

ISSN | 0024-6107 |

DOIs | |

Publication status | Published - 2015 |

### Bibliographical note

(Submitted on 28 Mar 2013 (v1), last revised 6 Sep 2013 (this version, v2))## Keywords

- math.DG

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