2004/06/10 by Christopher R. Lee, Lee, Christopher R.
Mathematics · #Geometry and complex manifolds #Geometric and Algebraic Topology #Geometric Analysis and Curvature Flows
paper · pdf · doi:10.48550/arxiv.math/0406225
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∖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.