New constructions of twistor lifts for harmonic maps

Martin Svensson, John C. Wood

Research output: Contribution to journalJournal articleResearchpeer-review

Abstract

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.
Original languageEnglish
JournalManuscripta Mathematica
Volume144
Issue number3-4
Pages (from-to)457-502
ISSN0025-2611
DOIs
Publication statusPublished - 2014

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Twistors
Harmonic Maps
Symmetric Spaces
Riemann Surface
Explicit Formula
If and only if

Keywords

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

Cite this

Svensson, Martin ; C. Wood, John. / New constructions of twistor lifts for harmonic maps. In: Manuscripta Mathematica. 2014 ; Vol. 144, No. 3-4. pp. 457-502.
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New constructions of twistor lifts for harmonic maps. / Svensson, Martin; C. Wood, John.

In: Manuscripta Mathematica, Vol. 144, No. 3-4, 2014, p. 457-502.

Research output: Contribution to journalJournal articleResearchpeer-review

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