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arXiv · 2011.13576

Existence of a complete holomorphic vector field via the K\"ahler-Einstein metric

Young-Jun Choi·Kang-Hyurk Lee
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Abstract

In this paper, we study the existence of a complete holomorphic vector fields on a strongly pseudoconvex complex manifold admitting a negatively curved complete K\"ahler-Einstein metric and a discrete sequence of automorphisms. Using the method of potential scaling, we will show that there is a potential function of the K\"ahler-Einstein metric whose differential has a constant length. Then we will construct a complete holomorphic vector field from the gradient vector field of the potential function.

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Young-Jun Choi, Kang-Hyurk Lee. 2020-11-27. Existence of a complete holomorphic vector field via the K\"ahler-Einstein metric. https://arxiv.org/abs/2011.13576

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