  An LCK (locally conformally Kahler) manifold is a complex manifold $(M,I)$
equipped with a Hermitian form $\omega$ and a closed 1-form $\theta$, called
the Lee form, such that $d\omega=\theta\wedge\omega$. An LCK manifold with
potential is an LCK manifold with a positive Kahler potential on its cover,
such that the deck group multiplies the Kahler potential by a constant. A Lee
class of an LCK manifold is the cohomology class of the Lee form. We determine
the set of Lee classes on LCK manifolds admitting an LCK structure with
potential, showing that it is an open half-space in $H^1(M,{\mathbb R})$. For
Vaisman manifolds, this theorem was proven in 1994 by Tsukada; we give a new
self-contained proof of his result.
