Journal of the Mathematical Society of Japan

Weierstrass-type representation for harmonic maps into general symmetric spaces via loop groups

Vladimir BALAN and Josef DORFMEISTER

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In [19] a method was presented, which constructs via loop group splittings all harmonic maps into a compact symmetric space. The present paper generalizes this method to all spaces G / K , where G is an arbitrary Lie group (semisimple or not) and K is the fixpoint group of some involution of G . The method is illustrated by a number of examples.

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J. Math. Soc. Japan, Volume 57, Number 1 (2005), 69-94.

First available in Project Euclid: 13 October 2006

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Primary: 58E20: Harmonic maps [See also 53C43], etc. 53C43: Differential geometric aspects of harmonic maps [See also 58E20] 22E67: Loop groups and related constructions, group-theoretic treatment [See also 58D05] 30F15: Harmonic functions on Riemann surfaces

harmonic map finite type harmonic map symmetric space Maurer-Cartan form Birkhoff splitting Iwasawa splitting affine connection loop group tangent group potential


BALAN, Vladimir; DORFMEISTER, Josef. Weierstrass-type representation for harmonic maps into general symmetric spaces via loop groups. J. Math. Soc. Japan 57 (2005), no. 1, 69--94. doi:10.2969/jmsj/1160745814.

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