Commuting Codazzi tensors and the Ribaucour transformation for submanifolds

DOI10.1007/BF03322986zbMath1055.53010OpenAlexW1993842342MaRDI QIDQ1430551

Marcos Dajczer, Ruy Tojeiro

Publication date: 27 May 2004

Published in: Results in Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf03322986

zbMATH Keywords

Ribaucour transformationCodazzi tensorCombescure transform

Mathematics Subject Classification ID

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

Related Items (14)

Ribaucour transformations and their singularities ⋮ On Ribaucour transformations and applications to linear Weingarten surfaces ⋮ The vectorial Ribaucour transformation for submanifolds and applications ⋮ A note on Ribaucour transformations in Lie sphere geometry ⋮ The Ribaucour transformation in Lie sphere geometry ⋮ The vectorial Ribaucour transformation for submanifolds of constant sectional curvature ⋮ The Ribaucour families of discrete R-congruences ⋮ Blaschke's problem for hypersurfaces ⋮ The Ribaucour transformation for hypersurfaces of two space forms and conformally flat hypersurfaces ⋮ Conformally flat submanifolds with flat normal bundle ⋮ A duality for conformally flat hypersurfaces ⋮ The Ribaucour transformation for flat Lagrangian submanifolds. ⋮ The codimension of submanifolds with negative extrinsic curvature ⋮ The dual superconformal surface

Cites Work

• Reducibility of Dupin submanifolds
• The Ribaucour transformation for flat Lagrangian submanifolds.
• AN EXTENSION OF THE CLASSICAL RIBAUCOUR TRANSFORMATION
• THE PATHS OF RAYS OF LIGHT IN GENERALIZED GENERAL RELATIVITY OF THE NONSYMMETRIC FIELD V ₄
• Lie sphere geometry. With applications to submanifolds
• Lagrangian submanifolds of constant sectional curvature and their Ribaucour transformation
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