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...

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Detalhes bibliográficos
Autores: Dajczer, Marcos, Tojeiro, Ruy
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
Descrição
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.