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Normal Variations of Invariant Hypersurfaces of Framed Manifolds

Published online by Cambridge University Press:  20 November 2018

Samuel I. Goldberg
Samuel I. Goldberg*
Affiliation:
University of Illinois, Urbana, Illinois
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A hypersurface of a globally framed f-manifold (briefly, a framed manifold), does not in general possess a framed structure as one may see by considering the 4-sphere S4 in R5 or S5. For, a hypersurface so endowed carries an almost complex structure, or else, it admits a nonsingular differentiable vector field. Since an almost complex manifold may be considered as being globally framed, with no complementary frames, this situation is in marked contrast with the well known fact that a hypersurface (real codimension 1) of an almost complex manifold admits a framed structure, more specifically, an almost contact structure.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 15 , Issue 4 , December 1972 , pp. 513 - 521
Copyright
Copyright © Canadian Mathematical Society 1972

References

1. Goldberg, S. I., Framed manifolds, Differential geometry, in honor of K. Yano, Kinokuniya, Tokyo (1972), 121-132.Google Scholar
2. Goldberg, S. I. and Yano, K., Noninvariant hypersurfaces of almost contact manifolds, J. Math. Soc. Japan, 22 (1970), 25-34.Google Scholar
3. Goldberg, S. I. and Yano, K., On normal globally framedfmanifolds, Tôhoku Math. J. 22 (1970), 362-370Google Scholar
4. Goldberg, S. I. and Yano, K., Globally framed f-manifolds, Illinois J. Math. 15 (1971), 456-474.Google Scholar