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Projectively Anosov flows with differentiable (un)stable foliations

Takeo Noda — 2000

Annales de l'institut Fourier

We consider projectively Anosov flows with differentiable stable and unstable foliations. We characterize the flows on T 2 which can be extended on a neighbourhood of T 2 into a projectively Anosov flow so that T 2 is a compact leaf of the stable foliation. Furthermore, to realize this extension on an arbitrary closed 3-manifold, the topology of this manifold plays an essential role. Thus, we give the classification of projectively Anosov flows on T 3 . In this case, the only flows on T 2 which extend to T 3 ...

Regular projectively Anosov flows with compact leaves

Takeo Noda — 2004

Annales de l’institut Fourier

This paper concerns projectively Anosov flows φ t with smooth stable and unstable foliations s and u on a Seifert manifold M . We show that if the foliation s or u contains a compact leaf, then the flow φ t is decomposed into a finite union of models which are defined on T 2 × 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 are incompressible...

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