The vectorial Ribaucour transformation for submanifolds and applications

DOI10.1090/S0002-9947-07-04211-0zbMath1124.53009arXivmath/0508217OpenAlexW2012309440WikidataQ126059944 ScholiaQ126059944MaRDI QIDQ5297037

Luis A. Florit, Marcos Dajczer, Ruy Tojeiro

Publication date: 17 July 2007

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

Full work available at URL: https://arxiv.org/abs/math/0508217

zbMATH Keywords

submanifoldsflat normal bundleDupin submanifoldsvectorial Ribaucour transformation

Mathematics Subject Classification ID

Local submanifolds (53B25) Correspondences and other transformation methods (e.g., Lie-Bäcklund) for PDEs on manifolds (58J72)

Related Items (8)

Ribaucour transformations and their singularities ⋮ On an algebro-geometric approach to Ribaucour transformations and Bianchi cubes ⋮ Einstein submanifolds with flat normal bundle in space forms are holonomic ⋮ The vectorial Ribaucour transformation for submanifolds of constant sectional curvature ⋮ Ribaucour coordinates ⋮ The Ribaucour families of discrete R-congruences ⋮ A connection between flat fronts in hyperbolic space and minimal surfaces in Euclidean space ⋮ Hypersurfaces of space forms carrying a totally geodesic foliation

Cites Work

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• AN EXTENSION OF THE CLASSICAL RIBAUCOUR TRANSFORMATION
• Vectorial Ribaucour transformations for the Lamé equations
• An algebraic formula for superposition and the completeness of the Bäcklund transformations of (2+1)-dimensional integrable systems
• Surfaces with flat normal bundle: An explicit construction

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