Let $\pi: M \to \Sigma$ be a circle bundle over a closed surface $\Sigma$. When does $M$ admit a contact form whose Reeb orbits are the fibres of this bundle?
2026-03-25 07:42:29.1774424549
Contact forms on circle bundles whose fibres are Reeb orbits
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These are known as Boothby-Wang fibrations. There are conditions that can be studied to say when your question can be positively answered. You can check Geiges Introduction to Contact Topology in Section 7.2.