Dressing orbits of harmonic maps
| dc.creator | Burstall, F. E. | |
| dc.creator | Pedit, F. | |
| dc.date | 1994-10-04 | |
| dc.date.accessioned | 2026-07-07T09:12:26Z | |
| dc.date.available | 2026-07-07T09:12:26Z | |
| dc.description | 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. | |
| dc.description | 28 pages, AmSLaTeX 1.1 | |
| dc.identifier | https://arxiv.org/abs/dg-ga/9410001 | |
| dc.identifier | http://arxiv.org/abs/dg-ga/9410001 | |
| dc.identifier | Duke Math. J. 80 1995 353-382 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/152017 | |
| dc.subject | Differential Geometry | |
| dc.title | Dressing orbits of harmonic maps | |
| dc.type | text |