Regular projectively Anosov flows with compact leaves
Annales de l'Institut Fourier, Volume 54 (2004) no. 2, p. 481-497

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 tori.

Cet article concerne les flots projectivement Anosov, dont les feuilletages stable et instable s et u sont lisses, sur une variété de Seifert M. Nous prouvons que si l’un des feuilletages s ou u contient une feuille compacte, alors le flot φ t se décompose en union finie de modèles définis sur T 2 ×I et ayant pour bord les feuilles compactes. La variété M est donc homeomorphe au tore T 3 . Dans la preuve, nous obtenons également un théorème qui classifie les feuilletages de codimension un sur les variétés de Seifert ayant des feuilles compactes qui sont des tores incompressibles.

DOI : https://doi.org/10.5802/aif.2026
Classification:  57R30,  37D30,  53C12,  53C15
Keywords: projectively Anosov flows, stable foliations, bi-contact structures
@article{AIF_2004__54_2_481_0,
     author = {Noda, Takeo},
     title = {Regular projectively Anosov flows with compact leaves},
     journal = {Annales de l'Institut Fourier},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {54},
     number = {2},
     year = {2004},
     pages = {481-497},
     doi = {10.5802/aif.2026},
     zbl = {1058.57021},
     language = {en},
     url = {http://www.numdam.org/item/AIF_2004__54_2_481_0}
}
Noda, Takeo. Regular projectively Anosov flows with compact leaves. Annales de l'Institut Fourier, Volume 54 (2004) no. 2, pp. 481-497. doi : 10.5802/aif.2026. http://www.numdam.org/item/AIF_2004__54_2_481_0/

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