Plane affine geometry and Anosov flows

We study Anosov flows on closed 3-manifolds. We define the notion of Anosov flows with the topological contact property (abreviation TCP Anosov flows): typical examples of TCP Anosov flows are contact Anosov flows, i.e. flows preserving a contact 1-form. We show that TCP Anosov flows are R-covered. The main tool is the study of the leaf spaces of lifted strong stable foliations: we exhibit on these leaf spaces a structure of (generalized) affine plane, in the sense of incidence geometry, (C) 2001 Editions scientifiques et medicales Elsevier SAS.