Submanifolds with nonparallel first normal bundle revisited
In this paper, we analyze the geometric structure of a Euclidean submanifold whose osculating spaces form a nonconstant family of proper subspaces of the same dimension. We prove that if the rate of change of the osculating spaces is small, then the submanifold must be a (submanifold of a) ruled sub...
| Autores: | , |
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| Tipo de documento: | artigo |
| Data de publicação: | 2014 |
| País: | España |
| Recursos: | Universitat Autònoma de Barcelona |
| Repositório: | Dipòsit Digital de Documents de la UAB |
| Idioma: | inglês |
| OAI Identifier: | oai:ddd.uab.cat:113933 |
| Acesso em linha: | https://ddd.uab.cat/record/113933 https://dx.doi.org/urn:doi:10.5565/PUBLMAT_58114_08 |
| Access Level: | Acceso aberto |
| Palavra-chave: | Euclidean submanifold First normal bundle |
| Resumo: | In this paper, we analyze the geometric structure of a Euclidean submanifold whose osculating spaces form a nonconstant family of proper subspaces of the same dimension. We prove that if the rate of change of the osculating spaces is small, then the submanifold must be a (submanifold of a) ruled submanifold of a very special type. We also give a sharp estimate of the dimension of the rulings. |
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