manuscripta mathematica

, Volume 51, Issue 1, pp 145–161

Deux remarques sur les flots riemanniens

  • Pierre Molino
  • Vlad Sergiescu

DOI: 10.1007/BF01168350

Cite this article as:
Molino, P. & Sergiescu, V. Manuscripta Math (1985) 51: 145. doi:10.1007/BF01168350


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 Hbn−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 Hbn−1(M,\(\mathfrak{F}\)) has a non trivial image in Hn−1(M).

Copyright information

© Springer-Verlag 1985

Authors and Affiliations

  • Pierre Molino
    • 1
  • Vlad Sergiescu
    • 2
  1. 1.Université Montpellier IIMontpellier CedexFrance
  2. 2.Université Lille IVilleneuve d'Ascq CedexFrance