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The vectorial Ribaucour transformation for submanifolds and applications
| Content Provider | Semantic Scholar |
|---|---|
| Author | Florit, Luis A. Dajczer, Marcos Tojeiro, Rita |
| Copyright Year | 2005 |
| Abstract | In 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 to provide an explicit local construction of an arbitrary Euclidean n-dimensional submanifold with flat normal bundle and codimension mby means of a commuting family of mHessian matrices on an open subset of Euclidean space Rn. Actually, this is a particular case of a more general result. Namely, we obtain a similar local 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. |
| Starting Page | 4977 |
| Ending Page | 4997 |
| Page Count | 21 |
| File Format | PDF HTM / HTML |
| DOI | 10.1090/S0002-9947-07-04211-0 |
| Alternate Webpage(s) | http://luis.impa.br/papers/ribvet.pdf |
| Alternate Webpage(s) | https://arxiv.org/pdf/math/0508217v1.pdf |
| Alternate Webpage(s) | http://arxiv.org/pdf/math/0508217v1.pdf |
| Alternate Webpage(s) | https://www.dm.ufscar.br/cursos/pos/preprintsDM/preprints2008/ribvettams.pdf |
| Alternate Webpage(s) | http://www.ams.org/journals/tran/2007-359-10/S0002-9947-07-04211-0/S0002-9947-07-04211-0.pdf |
| Alternate Webpage(s) | https://doi.org/10.1090/S0002-9947-07-04211-0 |
| Volume Number | 359 |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
