Existence of conformal symplectic foliations on closed manifolds

Abstract

AbstractWe study the existence of symplectic and conformal symplectic (codimension-1) foliations on closed manifolds of dimension $$\ge 5$$ ≥ 5 . Our main theorem, based on a recent result by Bertelson–Meigniez, states that in dimension at least 7 any almost contact structure is homotopic to a conformal symplectic foliation. In dimension 5 we construct explicit conformal symplectic foliations on every closed, simply-connected, almost contact manifold, as well as honest symplectic foliations on a large subset of them. Lastly, via round-connected sums, we obtain, on closed manifolds, examples of conformal symplectic foliations which admit a linear deformation to contact structures.