The vectorial Ribaucour transformation for submanifolds and applications

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dc.creatorFlorit, L.
dc.creatorDajczer, M.
dc.creatorTojeiro, R.
dc.date2005-08-12
dc.date.accessioned2026-07-07T05:22:19Z
dc.date.available2026-07-07T05:22:19Z
dc.descriptionIn this paper we develop the vectorial Ribaucour transformation for Euclidean submanifolds. We prove a general decomposition theorem showing that under {appropriate} conditions the composition of two or more vectorial Ribaucour transformations is again a vectorial Ribaucour transformation. An immediate consequence of this result is the classical permutability of Ribaucour transformations. Our main application is an explicit local construction of all Euclidean submanifolds with flat normal bundle. Actually, this is a particular case of a more general result. Namely, we obtain a local explicit construction of all Euclidean submanifolds carrying a parallel flat normal subbundle, in particular of all those that carry a parallel normal vector field. Finally, we describe all submanifolds carrying a Dupin principal curvature normal vector field with integrable conullity, a concept that has proven to be crucial in the study of reducibility of Dupin submanifolds.
dc.description24 pages
dc.identifierhttps://arxiv.org/abs/math/0508217
dc.identifierhttp://arxiv.org/abs/math/0508217
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/76018
dc.subjectDifferential Geometry
dc.subject53B25, 58J72
dc.titleThe vectorial Ribaucour transformation for submanifolds and applications
dc.typetext

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