Tableaux over Lie algebras, integrable systems, and classical surface theory

Details Tableaux over Lie algebras, integrable systems, and classical surface theory Tableaux over Lie algebras, integrable systems, and classical surface theory

2004-12-08

arxiv.org/abs/math/0412169v3

Comm. Anal. Geom. 14 (2006), no. 3, 475-496

Mathematics

Differential Geometry

16 pages, v3: final version; changes in the exposition

Scientific paper

Starting from suitable tableaux over finite dimensional Lie algebras, we provide a scheme for producing involutive linear Pfaffian systems related to various classes of submanifolds in homogeneous spaces which constitute integrable systems. These include isothermic surfaces, Willmore surfaces, and other classical soliton surfaces. Completely integrable equations such as the G/G_0-system of Terng and the curved flat system of Ferus-Pedit may be obtained as special cases of this construction. Some classes of surfaces in projective differential geometry whose Gauss-Codazzi equations are associated with tableaux over sl(4,R) are discussed.

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