Journal of Geometry

, 109:12 | Cite as

A note on the spectral deformation of harmonic maps from \({\varvec{S}}^{\varvec{2}}\) into the unitary group

Article

Abstract

In Ferreira et al. (Math Z 266:953–978, 2010), together with J. C. Wood, the authors gave a completely explicit formula for all harmonic maps from 2-spheres to the unitary group U(n) in terms of freely chosen meromorphic functions on \(S^2\). The simplest harmonic maps are the isotropic ones. Using Morse theory Burstall and Guest (Math Ann 309:541–572, 1997) showed that the harmonic maps are partitioned into classes labeled by the isotropic ones. In this work, using the formula for harmonic maps aforementioned, we describe explicitly this procedure, showing how all harmonic maps can be built from the isotropic ones.

Keywords

Harmonic map uniton loop group 

Mathematics Subject Classification

Primary 58E20 Secondary 53C43 

Notes

Acknowledgements

The authors would like to thank the referee for valuable corrections and suggestions. This work was partially supported by Fundação para a Ciência e Tecnologia, Portugal.

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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Maria João Ferreira
    • 1
    • 2
  • Bruno Ascenso Simões
    • 1
    • 2
  1. 1.Departamento de Matemática, Faculdade de CiênciasUniversidade de LisboaLisbonPortugal
  2. 2.Centro de Matemática e Aplicações FundamentaisUniversidade de LisboaLisbonPortugal

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