Locally conformally Kahler manifolds admitting a holomorphic conformal flow

TL;DR

This paper studies locally conformally Kahler manifolds with holomorphic conformal flows, proving such manifolds admit an automorphic potential, which advances understanding of their geometric structure.

Contribution

It demonstrates that LCK manifolds with a holomorphic conformal flow necessarily admit an automorphic potential, clarifying their geometric properties.

Findings

LCK manifolds with a holomorphic conformal flow admit an automorphic potential

The result corrects previous errors in the original publication

Provides new insights into the structure of LCK manifolds with symmetries

Abstract

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.