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.

Keywords

• locally conformally kähler manifold
• solvable lie group
• solvmanifold
• 53b35
• 53a30
• 22e25