Locally conformally Kahler manifolds admitting a holomorphic conformal flow

Abstract

A manifold $M$ is locally conformally Kahler (LCK) if it admits a Kahler covering with monodromy acting by holomorphic homotheties. Let $M$ be an LCK manifold admitting a holomorphic conformal flow of diffeomorphisms, lifted to a non-isometric homothetic flow on its covering. We show that $M$ admits an automorphic potential. This version was added 10 years after publication to correct some errors in the original.

9 pages, v. 3.0, some errors corrected (see arXiv:1601.07413 for details)