Regular projectively Anosov flows on three-dimensional manifolds

Asaoka, Masayuki

Annales de l'Institut Fourier, Tome 60 (2010) no. 5, pp. 1649-1684.

Nous classifions complètement les flots projectivement Anosov réguliers en dimension trois. Plus précisément, nous prouvons qu’un tel flot est un flot d’Anosov ou se décompose en une union finie de $T^2\times I$-modèles. Nous appliquons aussi notre méthode au problème de rigidité de certaines actions de groupes.

We give the complete classification of regular projectively Anosov flows on closed three-dimensional manifolds. More precisely, we show that such a flow must be either an Anosov flow or decomposed into a finite union of $T^2\times I$-models. We also apply our method to rigidity problems of some group actions.

Classification : 37D30, 57R30
Keywords: Projectively Anosov flows, bi-contact structures
Mot clés : flots projectivement Anosov, structures de bi-contact

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