A Boothby-Wang theorem for Besse contact forms.

We prove a Boothby-Wang type theorem for Besse Reeb flows that are not necessarily Zoll, i.e. Reeb flows all of whose orbits are periodic, but possibly with different periods. More precisely, we characterize contact manifolds whose Reeb flows are Besse as principal circle-orbibundles over integral symplectic orbifolds satisfying some cohomological condition. As a corollary of this and of a result by Cristofaro-Gardiner and Mazzucchelli we obtain a complete classification of closed Besse contact 3-manifolds up to strict contactomorphism.