Toric integrable geodesic flows in odd dimensions

Abstract

Let $Q$ be a compact, connected $n$-dimensional Riemannian manifold, and assume that the geodesic flow is toric integrable. If $n\ne 3$ is odd, or if ${\pi }_1(Q)$ is infinite, we show that the cosphere bundle of $Q$ is equivariantly contactomorphic to the cosphere bundle of the torus $\T^n$. As a consequence, $Q$ is homeomorphic to $\T^n$.

8 pages

References in corpus (4)

• Ricci flow with surgery on three-manifolds
• A Note on Toric Contact Geometry
• Completion of the Proof of the Geometrization Conjecture
• 3-Manifolds admitting toric integrable geodesic flows