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Formes de contact invariantes sur les 3-variétés. (Invariant contact forms on 3-manifolds). (French) Zbl 0569.57014

The author gives necessary and sufficient conditions for the existence of a contact form with associated vector field defined by a locally free \(S^ 1\)-action on a 3-dimensional manifold (dynamical system with all orbits closed). This apparently generalises known results, since no assumption is made about the space of orbits being a smooth surface. The condition is what one expects, namely that the orbits of the dynamical system admit no complementary foliation, which is \(S^ 1\)-invariant.
Reviewer: C.B.Thomas

MSC:

57R30 Foliations in differential topology; geometric theory
53C15 General geometric structures on manifolds (almost complex, almost product structures, etc.)
57S15 Compact Lie groups of differentiable transformations
57N10 Topology of general \(3\)-manifolds (MSC2010)
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