Locally conformally Kähler manifolds admitting a holomorphic conformal flow

摘要

A manifold $M$ is locally conformally Kahler if it admits a Kahler coveringwith monodromy acting by holomorphic homotheties. Let $M$ be an LCK manifoldadmitting a holomorphic conformal flow of diffeomorphisms, lifted to anon-isometric homothetic flow on the covering. We show that $M$ admits anautomorphic potential, and the monodromy group of its conformal weight bundleis $Z$.