THE BIANCHI–DARBOUX TRANSFORM OF L-ISOTHERMIC SURFACES

DOI10.1142/S0129167X00000465zbMath0979.53010arXivmath/0001062OpenAlexW2000317913MaRDI QIDQ4521174

Lorenzo Nicolodi, Emilio Musso

Publication date: 26 February 2002

Published in: International Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0001062

zbMATH Keywords

isothermic surfacesBäcklund transformationLaguerre geometrypermutability theoremBianchi-Darboux transformation

Mathematics Subject Classification ID

Related Items (15)

A class of surfaces related to a problem posed by Élie Cartan ⋮ Lie applicable surfaces and curved flats ⋮ Deformation and applicability of surfaces in Lie sphere geometry ⋮ Holomorphic differentials and Laguerre deformation of surfaces ⋮ Infinitesimal Darboux transformation and semi-discrete MKDV equation ⋮ Laguerre geometry of hypersurfaces in \({\mathbb R}^n\) ⋮ Discrete Ω$\Omega$‐nets and Guichard nets via discrete Koenigs nets ⋮ Laguerre isothermic surfaces in \(\mathbb R^3\) and their Darboux transformation ⋮ Isothermic surfaces in sphere geometries as Moutard nets ⋮ Classification of hypersurfaces with constant Laguerre eigenvalues in \(\mathbb R^{n }\) ⋮ Polynomial conserved quantities of Lie applicable surfaces ⋮ Laguerre minimal surfaces in \(\mathbb R^{3}\) ⋮ Classification of hypersurfaces with parallel Laguerre second fundamental form in \(\mathbb R^n\) ⋮ Laguerre isopararmetric hypersurfaces in \(\mathbb{R}^4\) ⋮ Weierstrass-type representations

Cites Work

• Bäcklund's theorem for \(n\)-dimensional submanifolds of \(R^{2n-1}\)
• An analogue of Bäcklund's theorem in affine geometry
• Curved flats in symmetric spaces
• Curved flats and isothermic surfaces
• The Darboux-Bianchi transformation for isothermic surfaces. Classical results versus the soliton approach
• Isothermic surfaces in \(\mathbf E^3\) as soliton surfaces
• Laguerre geometry of surfaces with plane lines of curvature
• A variational problem for surfaces in Laguerre geometry

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