Locally conformally Kähler manifolds admitting a holomorphic conformal flow

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Date
2010-03-15MFO Scientific Program
Research in Pairs 2010Series
Oberwolfach Preprints;2010,13Author
Ornea, Liviu
Verbitsky, Misha
Metadata
Show full item recordOWP-2010-13
Abstract
A manifold $M$ is locally conformally Kähler (LCK) if it admits a Kähler covering $\tilde{M}$ 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 $\tilde{M}$. We show that $M$ admits an automorphic potential, and the monodromy group of its conformal weight bundle is $\mathbb{Z}$.