On Bäcklund and Ribaucour transformations for surfaces with constant negative curvature

DOI10.1007/s10711-015-0113-5zbMath1360.53013OpenAlexW2182012144MaRDI QIDQ280122

Keti Tenenblat, Claudiano Goulart

Publication date: 29 April 2016

Published in: Geometriae Dedicata (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10711-015-0113-5

zbMATH Keywords

surfacesBäcklund transformationGaussian curvatureRibaucour transformation

Mathematics Subject Classification ID

Soliton equations (35Q51) Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42) Surfaces in Euclidean and related spaces (53A05) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21) Correspondences and other transformation methods (e.g., Lie-Bäcklund) for PDEs on manifolds (58J72)

Related Items (4)

Ribaucour transformations and their singularities ⋮ Unnamed Item ⋮ Caustics of pseudo-spherical surfaces in the Euclidean 3-space ⋮ Polynomial conserved quantities of Lie applicable surfaces

Cites Work

• Lie geometry of linear Weingarten surfaces
• Remarks on the Darboux transform of isothermic surfaces
• Ribaucour transformations revisited
• Minimal surfaces obtained by Ribaucour transformations
• Ribaucour transformations for constant mean curvature and linear Weingarten surfaces.
• Ribaucour transformations for flat surfaces in the hyperbolic 3-space
• New constant mean curvature surfaces in the hyperbolic space
• The Ribaucour transformation in Lie sphere geometry
• Ribaucour transformations for hypersurfaces in space forms
• Lawson correspondence and Ribaucour transformations
• AN EXTENSION OF THE CLASSICAL RIBAUCOUR TRANSFORMATION
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• Unnamed Item

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