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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:, [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.

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

[Dai] Dajczer, M., Euclidean submanifolds with nonparallel normal space, Math. Z. 204(1990), 551–557.Google Scholar
[Da2] Dajczer, M. et al., Submanifolds and Isometric Immersions, Math. Lecture Series 13, Publish or Perish Inc., Houston, 1990.Google Scholar
[D-N.] Dillen, F. and Nölker, S., Semi-parallel multi-rotation surfaces and the helix-property, J. Reine Angew. Math. 435(1993), 33–63.Google Scholar
[D-T.] Dajczer, M. and Tojeiro, R., On compositions of isometric immersions, J. Differential Geom. 36(1992), 1–18.Google Scholar
[G-M.] Griffone, J. and Morvan, J. M., External curvatures and internal torsion of a Riemannian submanifold, J. Differential Geom. 16(1981), 351–371.Google Scholar
[R-T.] Rodriguez, L. and Tribuzy, R., Reduction of codimension of regular immersions, Math. Z. 185(1984), 321–331.Google Scholar
[Sp] Spivak, M., A Comprehensive Introduction to Differential Geometry, Vol. 4, Publish or Perish Inc., Houston, 1979.Google Scholar