Locally conformally Kähler solvmanifolds: A survey

Abstract

A Hermitian structure on a manifold is called locally conformally Kähler (LCK) if it locally admits a conformal change which is Kähler. In this survey we review recent results of invariant LCK structures on solvmanifolds and present original results regarding the canonical bundle of solvmanifolds equipped with a Vaisman structure, that is, a LCK structure whose associated Lee form is parallel.