Abstract
Let Q be a compact, connected n-dimensional Riemannian manifold, and assume that the geodesic flow is toric integrable. If n 6= 3 is odd, or if π1(Q) is infinite, we show that the cosphere bundle of Q is equivariantly contactomorphic to the cosphere bundle of the torus Tn. As a consequence, Q is homeomorphic to Tn.
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