Bifurcations and global stability of families of gradients

M. J. Dias Carneiro; Jacob Palis

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Regular projectively Anosov flows with compact leaves

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This paper concerns projectively Anosov flows $φ^{t}$ with smooth stable and unstable foliations $ℱ^{s}$ and $ℱ^{u}$ on a Seifert manifold $M$ . We show that if the foliation $ℱ^{s}$ or $ℱ^{u}$ contains a compact leaf, then the flow $φ^{t}$ is decomposed into a finite union of models which are defined on $T^{2} \times I$ and bounded by compact leaves, and therefore the manifold $M$ is homeomorphic to the 3-torus. In the proof, we also obtain a theorem which classifies codimension one foliations on Seifert manifolds with compact leaves which...