3-Manifolds admitting toric integrable geodesic flows

Details 3-Manifolds admitting toric integrable geodesic flows 3-Manifolds admitting toric integrable geodesic flows

2004-06-10

arxiv.org/abs/math/0406225v2

Mathematics

Differential Geometry

9 pages, corrected and revised

Scientific paper

The geodesic flow of a Riemannian metric on a compact manifold $Q$ is said to be toric integrable if it is completely integrable and the first integrals of motion generate a homogeneous torus action on the punctured cotangent bundle $T^*Q\setminus{Q}$. If the geodesic flow is toric integrable, the cosphere bundle admits the structure of a contact toric manifold. By comparing the Betti numbers of contact toric manifolds and cosphere bundles, we are able to provide necessary conditions for the geodesic flow on a compact, connected 3-dimensional manifold to be toric integrable.

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