, Volume 51, Issue 1-3, pp 145-161

Deux remarques sur les flots riemanniens

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Abstract

Let M be a connected oriented closed n-manifold. A riemannian flow \(\mathfrak{F}\) on M is an oriented one dimensional foliation which admits a bundle-like metric.

We give a caracterization of isometric flows as riemannian flows whose basic cohomology H b n−1 (M, \(\mathfrak{F}\) ) is non trivial in degree (n−1). A second caracterization involves the triviality of the central sheaf.

We show also that \(\mathfrak{F}\) has a section if and only if H b n−1 (M, \(\mathfrak{F}\) ) has a non trivial image in Hn−1(M).