A note on toric contact geometry (Q5931237)

A contact manifold \(M\) of dimension \(2n+1\) is called a toric contact manifold if there is an effective \((n+1)\)-dimensional torus action on \(M\) that preserves a contact 1-form. If, in addition, the associated Reeb vector field corresponds to an element of the Lie algebra of this torus action, we say that \(M\) is a toric contact manifold of Reeb type. In this paper, the authors prove that every toric contact manifold of Reeb type can be obtained by so-called contact reduction from an odd dimensional sphere.