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When is an Anosov flow geodesic?

Published online by Cambridge University Press:  19 September 2008

Leon W. Green
Leon W. Green
Affiliation:
School of Mathematics, University of Minnesota, Minneapolis, MN 55455, USA
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Abstract

Let X, H+, H− be vector fields tangent, respectively, to an Anosov flow and its expanding and contracting foliations in a compact three-dimensional manifold, with γ, α+, α− one forms dual to them. If α+([H+, H−]) = α−([H+, H−]) and γ([H+, H−]) = α−([X, H−]) − α+([X, H+]), then the manifold has the structure of the unit tangent bundle of a Riemannian orbifold with geodesic flow field X.

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Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 12 , Issue 2 , June 1992, pp. 227 - 232
Copyright
Copyright © Cambridge University Press 1992

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