Locally conformally Kahler manifolds admitting a holomorphic conformal flow

Liviu Ornea, Misha Verbitsky
Arxiv ID: 1004.4645Last updated: 3/1/2021
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.

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