Currents on locally conformally K\"ahler manifolds

TL;DR

This paper characterizes the existence of locally conformally K"ahler metrics on compact complex manifolds using currents, extending Harvey and Lawson's classical results from K"ahler to locally conformally K"ahler geometry.

Contribution

It adapts the Harvey-Lawson characterization of K"ahler metrics to the locally conformally K"ahler setting for compact complex manifolds.

Findings

Provides a current-based criterion for locally conformally K"ahler metrics.

Extends classical K"ahler characterization to a broader class of complex manifolds.

Abstract

We characterize the existence of a locally conformally K\"ahler metric on a compact complex manifold in terms of currents, adapting the celebrated result of Harvey and Lawson for K\"ahler metrics.