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An application of the Morse theory to foliated manifolds

Published online by Cambridge University Press:  22 January 2016

Kazuhiko Fukui
Kazuhiko Fukui*
Affiliation:
Mathematical Institute, Kyoto University
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In [5], R. Thorn has started the study of the foliated structures by using the Morse theory. Recently K. Yamato [7] has studied the topological properties of leaves of a codimension one foliated manifold by investigating the “critical points” of variation equation of the given one-form.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 54 , July 1974 , pp. 165 - 178
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1974

References

[1] Milnor, J., Lectures on the h-cobordism theorem, Princeton, 1965.CrossRefGoogle Scholar
[2] Pontrjagin, L. S., Characteristic cycles on differentiable manifolds, A.M.S. Trans., Ser. 1, Vol. 7.Google Scholar
[3] Reeb, G., Sur certaines propriétés topologiques des variétés feuilletées, Actual. Sci. Ind., Hermann, Paris, 1183 (1952), 93–154.Google Scholar
[4] Reinhart, B. L., Foliated manifolds with bundle-like metrics, Ann. of Math., 8 (1959), 119–131.CrossRefGoogle Scholar
[5] Thorn, R., Généralisation de la théorie de Morse aux variétés feuilletées, Ann. Inst. Fourier, 14–1 (1964), 173–190.Google Scholar
[6] Thorn, R., Les singularités des applications differentiates, Ann. Inst. Fourier, 6 (1956), 45–87.Google Scholar
[7] Yamato, K., Qualitative theory of codimension one foliation, Nagoya Math. J., 49 (1973) 155–229.Google Scholar