The Darboux-Bianchi transformation for isothermic surfaces. Classical results versus the soliton approach

DOI10.1016/S0926-2245(97)00002-8zbMath0982.53003WikidataQ115337562 ScholiaQ115337562MaRDI QIDQ1360115

Jan L. Cieśliński

Publication date: 8 April 2002

Published in: Differential Geometry and its Applications (Search for Journal in Brave)

zbMATH Keywords

isothermic surfacesDarboux transformationDarboux matrixdual surfaceChristoffel transformsoliton surfacesisothermic immersionsSym formula

Mathematics Subject Classification ID

Clifford algebras, spinors (15A66) Surfaces in Euclidean and related spaces (53A05) Lie-Bäcklund and other transformations for infinite-dimensional Hamiltonian and Lagrangian systems (37K35)

Related Items (8)

THE BIANCHI–DARBOUX TRANSFORM OF L-ISOTHERMIC SURFACES ⋮ Lax triples for integrable surfaces in three-dimensional space ⋮ The cross ratio and Clifford algebras ⋮ Isothermic surfaces associated with the cylinder obtained by Ribaucour transformations ⋮ On a stack of surfaces obtained from the $\boldsymbol {\mathbb{C}P^{N-1}}$ sigma models ⋮ Group interpretation of the spectral parameter. The case of isothermic surfaces. ⋮ Isothermic submanifolds ⋮ Darboux-Bäcklund Transformations for Spin-Valued Linear Problems

Cites Work

• Algebraic representation of the linear problem as a method to construct the Darboux-Bäcklund transformation.
• The reduction problem and the inverse scattering method
• Curved flats and isothermic surfaces
• Isothermic surfaces in \(\mathbf E^3\) as soliton surfaces
• An effective method to compute N-fold Darboux matrix and N-soliton surfaces
• An algebraic method to construct the Darboux matrix
• Discrete isothermic surfaces.
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