Projectively Anosov flows with differentiable (un)stable foliations
Annales de l'Institut Fourier, Volume 50 (2000) no. 5, p. 1617-1647

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 (in the above way) are the linear flows.

On considère les flots projectivement Anosov dont les feuilletages stable et instable sont différentiables. On caractérise d’abord les flots sur T 2 qui, au voisinage de T 2 , admettent une extension en un flot projectivement Anosov, telle que T 2 soit une feuille compacte du feuilletage stable de ce flot. Si on veut, de plus, réaliser cette extension sur une variété fermée quelconque de dimension 3, la topologie de cette variété joue un rôle essentiel. On classifie ainsi les flots projectivement Anosov sur T 3 . Dans ce cas, les seuls flots sur T 2 qui s’étendent (comme ci-dessus) à T 3 sont des flots linéaires.

@article{AIF_2000__50_5_1617_0,
     author = {Noda, Takeo},
     title = {Projectively Anosov flows with differentiable (un)stable foliations},
     journal = {Annales de l'Institut Fourier},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {50},
     number = {5},
     year = {2000},
     pages = {1617-1647},
     doi = {10.5802/aif.1802},
     zbl = {01528717},
     mrnumber = {2001m:37055},
     language = {en},
     url = {http://www.numdam.org/item/AIF_2000__50_5_1617_0}
}
Noda, Takeo. Projectively Anosov flows with differentiable (un)stable foliations. Annales de l'Institut Fourier, Volume 50 (2000) no. 5, pp. 1617-1647. doi : 10.5802/aif.1802. http://www.numdam.org/item/AIF_2000__50_5_1617_0/

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