# Locally conformal K\"ahler structures on compact solvmanifolds

## Marcos Origlia

created by daniele on 09 Sep 2017
modified on 12 Sep 2017

3 oct 2017 -- 14:30

Aula Tricerri, DiMaI, Firenze

Abstract.

We consider locally conformal K\"ahler (LCK) manifolds, that is, a Hermitian manifold $(M, J, g)$ such that on each point there exists a neighborhood where the metric is conformal to a K\"ahler metric. Equivalently, $(M, J, g)$ is LCK if and only if there exists a closed $1$-form $\theta$ such that $d\omega = \theta \wedge \omega$, where $\omega$ is the fundamental $2$-form determined by the Hermitian structure. The $1$-form $\theta$ is called the Lee form.

In this work we study left invariant LCK structures on solvable Lie groups and the existence of lattices (co-compact discrete subgroups) on these Lie groups in order to obtain compact solvmanifolds equipped with these kind of locally conformal geometric structures.

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