Tight contact structures and Anosov flows (Q1862053)

In this paper, the authors observe a relationship between tight contact structures and Anosov flows on \(3\)-manifolds. A key tool is the result of \textit{Y. Mitsumatsu} [Ann. Inst. Fourier 45, 1407-1421 (1995; Zbl 0834.53031)] that the generator of an Anosov flow on a compact \(3\)-manifold is contained in the intersection of a pair of tight contact structures. Using this and Gompf's \(3\)-manifold invariant \(\theta\), they obtain a simple (up to these prerequisites) proof of the fact that \(S^3\) has no Anosov flows. Some other questions are also considered.