Abstract:This paper is devoted to studying a notion of Bott integrability for Reeb flows on contact 3‐manifolds. We show, in analogy with work of Fomenko–Zieschang on Hamiltonian flows in dimension 4, that Bott‐integrable Reeb flows exist precisely on graph manifolds. We also show that all ‐invariant contact structures on Seifert manifolds, as well as all contact structures on the 3‐sphere, on the 3‐torus and on , admit Bott‐integrable Reeb flows. Along the way, we establish some general Liouville‐type theorems for Bot… Show more
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