  A manifold M is locally conformally Kahler (LCK) if it admits a Kahler
covering with monodromy acting by holomorphic homotheties. For a compact
connected group G acting on an LCK manifold by holomorphic automorphisms, an
averaging procedure gives a G-invariant LCK metric. Suppose that U(1) acts on
an LCK manifold M by holomorphic isometries, and the lifting of this action to
the Kahler cover of M is not isometric. We show that the cover admits an
automorphic Kahler potential, and hence can be embedded to a Hopf manifold.
