Locally conformally Kahler manifolds admitting a holomorphic conformal flow

Details Locally conformally Kahler manifolds admitting a holomorphic conformal flow Locally conformally Kahler manifolds admitting a holomorphic conformal flow

2010-04-26

arxiv.org/abs/1004.4645v2

Mathematics

Differential Geometry

9 pages, v. 2.1, minor changes and clarifications from the referee, a proof of Corollary 2.1 added

Scientific paper

A manifold $M$ is locally conformally Kahler 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 the covering. We show that $M$ admits an automorphic potential, and the monodromy group of its conformal weight bundle is $\Z$.

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