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Actions of loop groups on the space of harmonic maps into reductive homogeneous spaces. (English) Zbl 0924.58013

It is shown that the so-called \(\nabla\)-harmonic maps from a Riemannian manifold to a reductive homogeneous space \(G/H\) endowed with the canonical connection are harmonic with respect to the invariant metric. It is proved also that there exist twisted loop group actions on the space of these maps when \(G/H\) is of compact type. The results are exemplified for the case \(G/H= SO(5)/SO(2)\times SO(2)\).

MSC:

58E20 Harmonic maps, etc.
37J35 Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests
37K10 Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.)
22E65 Infinite-dimensional Lie groups and their Lie algebras: general properties
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