Article

manuscripta mathematica

, Volume 51, Issue 1, pp 145-161

Deux remarques sur les flots riemanniens

  • Pierre MolinoAffiliated withUniversité Montpellier II
  • , Vlad SergiescuAffiliated withUniversité Lille I

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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).