### Abstract

Original language | English |
---|---|

Journal | Manuscripta Mathematica |

Volume | 144 |

Issue number | 3-4 |

Pages (from-to) | 457-502 |

ISSN | 0025-2611 |

DOIs | |

Publication status | Published - 2014 |

### Fingerprint

### Keywords

- math.DG
- 53C43 (Primary) 58E20 (Secondary)

### Cite this

*Manuscripta Mathematica*,

*144*(3-4), 457-502. https://doi.org/10.1007/s00229-014-0659-9

}

*Manuscripta Mathematica*, vol. 144, no. 3-4, pp. 457-502. https://doi.org/10.1007/s00229-014-0659-9

**New constructions of twistor lifts for harmonic maps.** / Svensson, Martin; C. Wood, John.

Research output: Contribution to journal › Journal article › Research › peer-review

TY - JOUR

T1 - New constructions of twistor lifts for harmonic maps

AU - Svensson, Martin

AU - C. Wood, John

PY - 2014

Y1 - 2014

N2 - 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.

AB - 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.

KW - math.DG

KW - 53C43 (Primary) 58E20 (Secondary)

U2 - 10.1007/s00229-014-0659-9

DO - 10.1007/s00229-014-0659-9

M3 - Journal article

VL - 144

SP - 457

EP - 502

JO - Manuscripta Mathematica

JF - Manuscripta Mathematica

SN - 0025-2611

IS - 3-4

ER -