Geodesic
Harmonic maps into loop spaces of compact Lie groups
Contemporary Mathematics. Fundamental Directions, Proceedings of the Fourth International Conference on Differential and Functional-Differential Equations (Moscow, August 14–21, 2005). Part 2, Tome 16 (2006), pp. 136-145 
A. G. Sergeev. Harmonic maps into loop spaces of compact Lie groups. Contemporary Mathematics. Fundamental Directions, Proceedings of the Fourth International Conference on Differential and Functional-Differential Equations (Moscow, August 14–21, 2005). Part 2, Tome 16 (2006), pp. 136-145. http://geodesic.mathdoc.fr/item/CMFD_2006_16_a8/
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     author = {A. G. Sergeev},
     title = {Harmonic maps into loop spaces of compact {Lie} groups},
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     year = {2006},
     volume = {16},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CMFD_2006_16_a8/}
}
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

We study harmonic maps from Riemann surfaces $M$ to the loop spaces $\Omega G$ of compact Lie groups $G$, using the twistor approach. Harmonic maps into loop spaces are of a special interest because of their relation to the Yang–Mills equations on $\mathbb R^4$.

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