Isothermic surfaces in $\E^3$ as soliton surfaces

Details Isothermic surfaces in $\E^3$ as soliton surfaces Isothermic surfaces in $\E^3$ as soliton surfaces

1995-02-14

arxiv.org/abs/solv-int/9502004v2

Mathematics

Differential Geometry

Revised version; 13 pages in LaTeX, 1 figure PostScript; to appear in Physics Letters A

Scientific paper

10.1016/0375-9601(95)00504-V

We show that the theory of isothermic surfaces in $\E^3$ -- 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 $\E^3$ 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.

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