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Pluriharmonic maps into outer symmetric spaces and a subdivision of Weyl chambers
Author(s) -
Eschenburg J.H.,
Mare A.L.,
Quast P.
Publication year - 2010
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/blms/bdq070
Subject(s) - mathematics , embedding , rank (graph theory) , manifold (fluid mechanics) , pure mathematics , symmetric space , subdivision , harmonic , mathematical analysis , combinatorics , physics , mechanical engineering , archaeology , artificial intelligence , computer science , engineering , history , quantum mechanics
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 r to 2 s 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’.