dorsal/arxiv
View SchemaIsothermic surfaces in $\E^3$ as soliton surfaces
| Authors | Jan Cieśliński, Piotr Goldstein, Antoni Sym |
|---|---|
| Categories | |
| ArXiv ID | solv-int/9502004 |
| URL | https://arxiv.org/abs/solv-int/9502004 |
| DOI | 10.1016/0375-9601(95)00504-V |
Abstract
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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"abstract": "We show that the theory of isothermic surfaces in $\\E^3$ -- one of the oldest\nbranches of differential geometry -- can be reformulated within the modern\ntheory of completely integrable (soliton) systems. This enables one to study\nthe geometry of isothermic surfaces in $\\E^3$ by means of powerful spectral\nmethods available in the soliton theory. Also the associated non-linear system\nis interesting in itself since it displays some unconventional soliton features\nand, physically, could be applied in the theory of infinitesimal deformations\nof membranes.",
"arxiv_id": "solv-int/9502004",
"authors": [
"Jan Cie\u015bli\u0144ski",
"Piotr Goldstein",
"Antoni Sym"
],
"categories": [
"solv-int",
"dg-ga",
"math.DG",
"nlin.SI"
],
"doi": "10.1016/0375-9601(95)00504-V",
"title": "Isothermic surfaces in $\\E^3$ as soliton surfaces",
"url": "https://arxiv.org/abs/solv-int/9502004"
},
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