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GEOMETRIC ANOSOV FLOWS OF DIMENSION FIVE WITH SMOOTH DISTRIBUTIONS

Published online by Cambridge University Press:  15 April 2005

Yong Fang
Yong Fang
Affiliation:
Laboratoire de Mathématique d’Orsay, UMR 8628 du CNRS, Université Paris-Sud, France (fangyong1@yahoo.fr)
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Abstract

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We classify the five-dimensional $C^\infty$ Anosov flows which have $C^\infty$-Anosov splitting and preserve a smooth pseudo-Riemannian metric. Up to a special time change and finite covers, such a flow is $C^\infty$ flow equivalent either to the suspension of a symplectic hyperbolic automorphism of $\mathbb{T}^{4}$, or to the geodesic flow on a three-dimensional hyperbolic manifold.

AMS 2000 Mathematics subject classification: Primary 34Cxx; 34Dxx; 37-XX

Keywords

Anosov flowpseudo-Riemannian metriclinear connectionergodicity
Type
Research Article
Information
Journal of the Institute of Mathematics of Jussieu , Volume 4 , Issue 3 , July 2005 , pp. 333 - 362
Copyright
2005 Cambridge University Press