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.