3-Manifolds admitting toric integrable geodesic flows

Abstract

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 $T^{\ast }Q\setminus Q$. 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.

9 pages, corrected and revised

References in corpus (2)

• L^p norms of eigenfunctions in the completely integrable case
• Period three actions on the three-sphere

Cited by in corpus (1)

• Toric integrable geodesic flows in odd dimensions