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Feuilletages riemanniens à croissance polynômiale. (Riemannian foliations with polynomial growth). (French) Zbl 0661.53022
The author gives necessary and sufficient conditions for a Riemannian foliation $${\mathcal F}$$ of a compact manifold M to be closed at infinity and to have a polynomial growth in terms of algebraic properties of the structural Lie algebra $${\mathfrak g}$$ of $${\mathcal F}$$. It is also shown that if $${\mathfrak g}$$ is nilpotent, then $$\delta$$ ($${\mathfrak g})\leq d({\mathcal F})$$ where $$\delta$$ ($${\mathfrak g})$$ is the degree of nilpotence of $${\mathfrak g}$$ and d($${\mathcal F})$$ is the degree of polynomial growth of $${\mathcal F}$$. The following facts are obtained as corollaries: the structural Lie algebra of a Riemannian flow on a compact manifold is abelian; a Riemannian foliation $${\mathcal F}$$ with polynomial growth on a compact manifold M is minimizable if and only if the basic cohomology of $${\mathcal F}$$ of maximal degree does not vanish.
Reviewer: A.Piatkowski

##### MSC:
 53C12 Foliations (differential geometric aspects) 57R30 Foliations in differential topology; geometric theory
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