Locally conformally SKT structures

As is well known, a Hermitian metric on a complex manifold is called SKT (strong K\”ahler with torsion) if the Bismut torsion form $H$ is such that $dH=0$. In this talk, as a conformal generalisation of the SKT condition, we will introduce a new type of Hermitian structure, called \emph{locally conformally SKT}. Precisely, a Hermitian structure $(J,g)$ is said to be locally conformally SKT if there exists a closed 1-form $\alpha$ such that $dH = \alpha \wedge H$. We will discuss the existence of such structures on Lie groups and their compact quotients by lattices. This is joint work with Anna Fino and Zineb Larbi.