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Submanifolds with Nonparallel First Normal Bundle

Published online by Cambridge University Press:  20 November 2018

Marcos Dajczer  and
Ruy Tojeiro
Marcos Dajczer
Affiliation:
IMPA, Estrada Dona Castorina 110, 22460-320 Rio de Janeiro, Brasil, e-mail:, MARCOS@impa.br
Ruy Tojeiro
Affiliation:
Universidade Federal de Uberlândia, 38400-020 Uberlândia, Brasil, e-mail:, DEMAT04@brufu.bitnet
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Abstract

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We provide a complete local geometric description of submanifolds of spaces with constant sectional curvature where the first normal spaces, that is, the subspaces spanned by the second fundamental form, form a vector subbundle of the normal bundle of low rank which is nonparallel in the normal connection. We also characterize flat submanifolds with flat normal bundle in Euclidean space satisfying the helix property.

Keywords

Primary: 53B25secondary: 53C40
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 37 , Issue 3 , 01 September 1994 , pp. 330 - 337
Copyright
Copyright © Canadian Mathematical Society 1994

References

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