Mathematical Research Letters

Volume 18 (2011)

Number 5

Toric Integrable Geodesic Flows in Odd Dimensions

Pages: 1013 – 1022



Christopher R. Lee

Susan Tolman


Let $Q$ be a compact, connected $n$-dimensional Riemannian manifold, and assume that the geodesic flow is toric integrable. If $n \neq 3$ 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 $\T^n$.

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