Reduction of locally conformal symplectic manifolds with examples of non-Kähler manifolds

Abstract

Let $(M, \Omega)$ be a locally conformal symplectic manifold. $\Omega$ is a non-degenerate 2-form on $M$ such that there is a closed 1-form $\omega$, called the Lee form, satisfing $ d\Omega=\omega\wedge\Omega$. In this paper we consider Marsden-Weinstein reduction theorem which induces Jacobi-Liouville theorem as a special case. For locally conformal Kähler manifolds, this reduction theorem gives a construction of non-Kähler manifolds in general dimension.