Reductions of locally conformal symplectic structures and de Rham cohomology tangent to a foliation

TL;DR

This paper introduces a reduction procedure for locally conformal symplectic structures applicable to many submanifolds, identifying global obstructions related to de Rham cohomology classes of the Lee form.

Contribution

It establishes a new reduction method for locally conformal symplectic structures and characterizes global obstructions via cohomology classes tangent to foliations.

Findings

Reduction procedure applicable to wide class of submanifolds

No local obstructions to the reduction process

Global obstructions characterized by specific de Rham cohomology classes

Abstract

We propose a produre of reduction a locally conformal symplectic structure. This procedure of reduction can be applied to wide class of submanifolds. There are no local obstructions for this procedure. But there are global obstructions. We find a necessary and sufficient condition when this reduction holds in terms of the special kind of de Rham cohomology class (tangent to the characteristic foliation) of the Lee form.