Publication Date
1995
Journal or Book Title
DUKE MATHEMATICAL JOURNAL
Abstract
We study the harmonic map equations for maps of a Riemann surface into a Riemannian symmetric space of compact type from the point of view of soliton theory. There is a well-known dressing action of a loop group on the space of harmonic maps and we discuss the orbits of this action through particularly simple harmonic maps called {\em vacuum solutions}. We show that all harmonic maps of semisimple finite type (and so most harmonic $2$-tori) lie in such an orbit. Moreover, on each such orbit, we define an infinite-dimensional hierarchy of commuting flows and characterise the harmonic maps of finite type as precisely those for which the orbit under these flows is finite-dimensional.
Pages
353-382
Volume
80
Issue
2
Recommended Citation
Burstall, FE and Pedit, F, "Dressing orbits of harmonic maps" (1995). DUKE MATHEMATICAL JOURNAL. 768.
Retrieved from https://scholarworks.umass.edu/math_faculty_pubs/768
Comments
This is the pre-published version harvested from arXiv. The published version is located at http://projecteuclid.org/DPubS?service=UI&version=1.0&verb=Display&handle=euclid.dmj/1077246087