Existence of a complete holomorphic vector field via the K\"ahler-Einstein metric
Complex Variables
2020-11-30 v1 Differential Geometry
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.
Keywords
Cite
@article{arxiv.2011.13576,
title = {Existence of a complete holomorphic vector field via the K\"ahler-Einstein metric},
author = {Young-Jun Choi and Kang-Hyurk Lee},
journal= {arXiv preprint arXiv:2011.13576},
year = {2020}
}