Let $(M, g, J)$ be a compact Hermitian manifold and $\Omega$ the fundamental 2-form of $(g, J)$. A Hermitian manifold $(M, g, J)$ is said to be locally conformal Kähler if there exists a closed 1-form $\omega$ such that $d\Omega=\omega \wedge \Omega$. The purpose of this paper is to investigate a relation between a locally conformal Kähler structure and the adapted differential operator on compact solvmanifolds.
"Locally conformal Kähler structures on compact solvmanifolds." Osaka J. Math. 49 (4) 1087 - 1102, December 2012.