Displaying similar documents to “Plane affine geometry and Anosov flows”

Projectively Anosov flows with differentiable (un)stable foliations

Takeo Noda (2000)

Annales de l'institut Fourier

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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...

Regular projectively Anosov flows with compact leaves

Takeo Noda (2004)

Annales de l’institut Fourier

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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 × 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...

Transversely affine foliations of some surface bundles over S 1 of pseudo-Anosov type

Hiromichi Nakayama (1991)

Annales de l'institut Fourier

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We consider transversely affine foliations without compact leaves of higher genus surface bundles over the circle of pseudo-Anosov type such that the Euler classes of the tangent bundles of the foliations coincide with that of the bundle foliation. We classify such foliations of those surface bundles whose monodromies satisfy a certain condition.

The Poincaré-Bendixson theorem and arational foliations on the sphere

Igor Nikolaev (1996)

Annales de l'institut Fourier

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Foliations on the 2-sphere with a finite number of non-orientable singularities are considered. For this class a Poincaré-Bendixson theorem is established. In particular, the work gives an answer to a problem of H. Rosenberg concerning labyrinths.