Holonomy Groups of Locally Conformally Kähler Metrics

A Hermitian metric on a complex manifold is locally conformally Kähler
if it is conformal to a Kähler metric in the neighbourhood of each point.
In this talk will be given the classification of the possible holonomy groups
of such metrics on compact manifolds. As a by-product, we present the geometric
description of conformal classes on compact manifolds containing two non-homothetic
Kähler metrics - necessarily with respect to non-conjugate complex structures.
The talk is based on joint work with Farid Madani and Andrei Moroianu, which is
available on arXiv: https://arxiv.org/abs/1511.09212.