Isothermic surfaces in $\E^3$ as soliton surfaces
solv-int
2009-10-28 v2 dg-ga
Differential Geometry
Exactly Solvable and Integrable Systems
Abstract
We show that the theory of isothermic surfaces in -- one of the oldest branches of differential geometry -- can be reformulated within the modern theory of completely integrable (soliton) systems. This enables one to study the geometry of isothermic surfaces in by means of powerful spectral methods available in the soliton theory. Also the associated non-linear system is interesting in itself since it displays some unconventional soliton features and, physically, could be applied in the theory of infinitesimal deformations of membranes.
Cite
@article{arxiv.solv-int/9502004,
title = {Isothermic surfaces in $\E^3$ as soliton surfaces},
author = {Jan Cieśliński and Piotr Goldstein and Antoni Sym},
journal= {arXiv preprint arXiv:solv-int/9502004},
year = {2009}
}
Comments
Revised version; 13 pages in LaTeX, 1 figure PostScript; to appear in Physics Letters A