Canonical metrics in complex geometry

Abstract

AbstractA Hermitian metric on a complex manifold is said to be pluriclosed or SKT if the torsion of the associated Bismut connection is closed, and it is called balanced if its fundamental form is co-closed. In the paper we give an overview of recent results on pluriclosed and balanced metrics, provide new constructions of compact non-Kähler manifolds and also present a few open problems.