| Locally conformally Kahler (LCK) metrics are generalizations of Kahler metrics in a conformal manner: a metric g is LCK if around every point of the manifold, g is conformal to a local Kahler metric. The symplectic counterpart of these structures is given by the locally conformally symplectic (LCS) forms. In the first part of this talk, I will give an introduction to this class of manifolds and discuss some of their main features. Then I will focus on toric LCS manifolds, which can be defined in analogy with toric symplectic geometry. I will present a classification result in the spirit of Delzant’s theorem, after which I will discuss some metric properties of toric LCK manifolds. |