Definition 23.2.248F6C713AFE3

Definition 23.2.2.48F6C713AFE3 A Hermitian form $\omega $ on $X$ is locally conformally Kähler, or LCK, if there is a smooth real one-form $\lambda $ on $X$ such that

The form $\lambda $ is called its Lee form. The metric is strictly LCK if $\lambda $ is not exact. A strictly LCK metric is Vaisman if its Lee form is parallel for the Levi–Civita connection of the associated Riemannian metric.