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Submanifolds with Nonparallel First Normal Bundle

Published online by Cambridge University Press:  20 November 2018

Marcos Dajczer
Affiliation:
IMPA, Estrada Dona Castorina 110, 22460-320 Rio de Janeiro, Brasil, e-mail:, [email protected]
Ruy Tojeiro
Affiliation:
Universidade Federal de Uberlândia, 38400-020 Uberlândia, Brasil, e-mail:, [email protected]
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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.

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 1994

References

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