A conformally Anosov Reeb flow on a contact 3-manifold forces universal tightness, irreducibility, and absence of exact cobordisms to the standard three-sphere, which therefore admits no such flow.
Homotopy classes of total foliations and bi-contact structures on three-manifolds
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abstract
On every compact and orientable three-manifold, we construct total foliations (three codimension 1 foliations that are transverse at every point). This construction can be performed on any homotopy class of plane fields with vanishing Euler class. As a corollary we obtain similar results on bi-contact structures.
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Dynamics and Topology of Conformally Anosov Contact 3-Manifolds
A conformally Anosov Reeb flow on a contact 3-manifold forces universal tightness, irreducibility, and absence of exact cobordisms to the standard three-sphere, which therefore admits no such flow.