Pluriharmonic maps into outer symmetric spaces and a subdivision of Weyl chambers

Burstall and Guest have given a classification of harmonic maps of the 2-sphere with values in Lie groups and inner symmetric spaces. We extend their result to outer symmetric spaces G/K, using the pointed Cartan embedding into G. We show that in this case the number of classes can be reduced from 2...

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Bibliographic Details
Published in:The Bulletin of the London Mathematical Society 2010-12, Vol.42 (6), p.1121-1133
Main Authors: Eschenburg, J.‐H., Mare, A.‐L., Quast, P.
Format: Article
Language:English
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Summary:Burstall and Guest have given a classification of harmonic maps of the 2-sphere with values in Lie groups and inner symmetric spaces. We extend their result to outer symmetric spaces G/K, using the pointed Cartan embedding into G. We show that in this case the number of classes can be reduced from 2r to 2s where r = rank G and s = rank K. Moreover we replace the 2-sphere by a simply connected compact Kähler manifold and ‘harmonic’ by ‘pluriharmonic’.
ISSN:0024-6093
1469-2120
DOI:10.1112/blms/bdq070