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Riemannian homogeneous foliations without holonomy

Published online by Cambridge University Press:  22 January 2016

Robert A. Blumenthal
Robert A. Blumenthal*
Affiliation:
Université des Sciences et Techniques de Lille I, U.E.R. de Mathématiques Pures et Appliquées, B.P. 36-59650 Villeneuve d’Ascq, France, Department of Mathematics, St. Louis University, St. Louis, Missouri 63103, U.S.A.
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Let M be a compact connected C∞ manifold with a smooth Riemannian foliation ℱ. That is, (M, ℱ) admits a bundle-like metric in the sense of [7]. In [4] it is shown that if all leaves of ℱ are closed without holonomy, then the space of leaves M/ℱ of the foliation is a manifold and the natural projection M → M/ℱ is a locally trivial fibre space. In the present work we show that for certain of the Riemannian homogeneous foliations, holonomy is the only obstruction to the foliation being a fibration.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 83 , October 1981 , pp. 197 - 201
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1981

References

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