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(o)-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.

Tableaux over Lie algebras, integrable systems, and classical surface theory / MUSSO E; NICOLODI L.. - In: COMMUNICATIONS IN ANALYSIS AND GEOMETRY. - ISSN 1019-8385. - 14:3(2006), pp. 475-496.

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

NICOLODI, Lorenzo
2006

Abstract

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(o)-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.
Tableaux over Lie algebras, integrable systems, and classical surface theory / MUSSO E; NICOLODI L.. - In: COMMUNICATIONS IN ANALYSIS AND GEOMETRY. - ISSN 1019-8385. - 14:3(2006), pp. 475-496.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11381/1485508
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