Locally conformally Kähler manifolds admitting a holomorphic conformal flow

Abstract

Abstract A manifold M is locally conformally Kähler (LCK) if it admits a Kähler covering ˜M 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 ˜M . We show that M admits an automorphic potential, and the monodromy group of its conformal weight bundle is Z.