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Duality and minimality in Riemannian foliations. (English) Zbl 0778.53029

Let \(M\) be a smooth closed orientable manifold and \({\mathcal F}\) an oriented Riemannian foliation on \(M\). The author proves that \({\mathcal F}\) is minimal if and only if the basic cohomology of maximal dimension is nonzero.

MSC:

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