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Existence of regular coverings associated with leaves of codimension one foliations

Published online by Cambridge University Press:  22 January 2016

Gikō Ikegami
Gikō Ikegami*
Affiliation:
Department of Mathematics, College of General Education, Nagoya University
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In this paper we are concerned with transversely orientable codimension one foliations. Let be a Cr-foliation as above in a smooth manifold M, r ≧ 1, and let F0 be a closed leaf of . A neighborhood U of F0 is called a bicollar of F0 in this paper if there is a normal line bundle : U → F0 with respect to a fixed Riemannian metric on M such that each fibre of is transverse to .

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 67 , August 1977 , pp. 15 - 34
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1977

References

[1] Hirsch, M., Stability of compact leaves of foliations, Dynamical Systems, ed. Peixoto, M., Academic Press, N.Y., 1973, 135–153.Google Scholar
[2] Levine, H. and Shub, M., Stability of foliations, Trans. A.M.S., 184 (1973), 419–437.CrossRefGoogle Scholar
[3] Nakatsuka, H., On representations of homology classes, Proc. Japan Acad., 48 (1972), 360–364.Google Scholar
[4] Nishimori, T., Compact leaves with abelian holonomy, Tōhoku Math. J. The Second Series, 27 (1975), 259–272.Google Scholar
[5] Sterenberg, S., Local Cn transformation of the real line, Duke Math. J., 24 (1957), 97–102.Google Scholar