  A locally conformally Kahler (LCK) manifold is a complex manifold admitting a
Kahler covering M, such that its monodromy acts on this covering by
homotheties. A compact LCK manifold is called LCK with potential if M admits an
authomorphic Kahler potential. It is known that in this case it is an algebraic
cone, that is, the set of all non-zero vectors in the total space of an
anti-ample line bundle over a projective orbifold. We start with an algebraic
cone C, and show that the set of Kahler metrics with potential which could
arise from an LCK structure is in bijective correspondence with the set of
pseudoconvex shells, that is, pseudoconvex hypersurfaces in C meeting each
orbit of the associated R-action exactly once. This is used to produce explicit
LCK and Vaisman metrics on Hopf manifolds, generalizing earlier work by
Gauduchon-Ornea and Kamishima-Ornea.
