Abstract
We show that for a smooth Anosov flow on a closed five dimensional manifold, if it has C ∞ Anosov splitting and preserves a C ∞ pseudo-Riemannian metric, then up to a special time change and finite covers, it is C ∞ flow equivalent either to the suspension of a symplectic hyperbolic automorphism of T 4 , or to the geodesic flow on a three dimensional hyperbolic manifold. To cite this article: Y. Fang, C. R. Acad. Sci. Paris, Ser. I 336 (2003).
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