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arXiv · 1012.0795

Toric integrable geodesic flows in odd dimensions

Christopher R. Lee·Susan Tolman
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Abstract

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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Christopher R. Lee, Susan Tolman. 2010-12-03. Toric integrable geodesic flows in odd dimensions. https://doi.org/10.4310/mrl.2011.v18.n5.a18

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