^{1} Department of Mathematics and Computer Science (IMADA), Faculty of Science, SDU^{2} Mathematics, Department of Mathematics and Computer Science (IMADA), Faculty of Science, SDU^{3} University of Leeds^{4} Department of Mathematics and Computer Science (IMADA), Faculty of Science, SDU

DOI:

10.1007/s00229-014-0659-9

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.

Type:

Journal article

Language:

English

Published in:

Manuscripta Mathematica, 2014, Vol 144, Issue 3-4, p. 457-502