On the Geometry of Almost S-Manifolds

Abstract EN

An f-structure on a manifold M is an endomorphism field φ satisfying φ3+φ=0.

We call an f-structure regular if the distribution T=ker φ is involutive and regular, in the sense of Palais.

We show that when a regular f-structure on a compact manifold M is an almost S-structure, it determines a torus fibration of M over a symplectic manifold.

When rank T=1, this result reduces to the Boothby-Wang theorem.

Unlike similar results for manifolds with S-structure or K-structure, we do not assume that the f-structure is normal.

We also show that given an almost S-structure, we obtain an associated Jacobi structure, as well as a notion of symplectization.