Lawson correspondence and Ribaucour transformations

DOI10.1090/S0002-9947-2012-05440-7zbMath1277.53055OpenAlexW2010659893MaRDI QIDQ2844837

Pedro Roitman, M. Lemes, Keti Tenenblat, Renato Tribuzy

Publication date: 20 August 2013

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0002-9947-2012-05440-7

zbMATH Keywords

sectional curvatureDarboux transformationsGaussian curvatureconstant mean curvature surfacesLawson correspondenceRibaucour transformationshorosphere type end

Mathematics Subject Classification ID

Minimal surfaces in differential geometry, surfaces with prescribed mean curvature (53A10) Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42) Global Riemannian geometry, including pinching (53C20) Lie-Bäcklund and other transformations for infinite-dimensional Hamiltonian and Lagrangian systems (37K35) Correspondences and other transformation methods (e.g., Lie-Bäcklund) for PDEs on manifolds (58J72)

Related Items (7)

Ribaucour transformations and their singularities ⋮ On Bäcklund and Ribaucour transformations for surfaces with constant negative curvature ⋮ Unnamed Item ⋮ New minimal surfaces in the hyperbolic space ⋮ Ribaucour type transformations for the Hessian one equation ⋮ A connection between flat fronts in hyperbolic space and minimal surfaces in Euclidean space ⋮ Ribaucour transformations for flat surfaces in the hyperbolic 3-space

Cites Work

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• Weierstrass type representation of harmonic maps into symmetric spaces
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• Ribaucour transformations for constant mean curvature and linear Weingarten surfaces.
• New constant mean curvature surfaces in the hyperbolic space
• Ribaucour transformations for hypersurfaces in space forms
• Complete minimal surfaces in \(S^ 3\)
• On the index of constant mean curvature 1 surfaces in hyperbolic space
• Asymptotics of ends of constant mean curvature surfaces with bubbletons
• On the geometry of constant mean curvature one surfaces in hyperbolic space

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