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Existence of a complete holomorphic vector field via the Kähler–Einstein metric
Annals of Global Analysis and Geometry ( IF 0.7 ) Pub Date : 2021-04-26 , DOI: 10.1007/s10455-021-09769-2 Young-Jun Choi , Kang-Hyurk Lee
中文翻译:
通过Kähler-Einstein度量完整的全纯矢量场的存在
更新日期:2021-04-26
Annals of Global Analysis and Geometry ( IF 0.7 ) Pub Date : 2021-04-26 , DOI: 10.1007/s10455-021-09769-2 Young-Jun Choi , Kang-Hyurk Lee
In this paper, we study the existence of a complete holomorphic vector field on a strongly pseudoconvex complex manifold admitting a negatively curved complete Kähler–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 Kähler–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.
中文翻译:
通过Kähler-Einstein度量完整的全纯矢量场的存在
在本文中,我们研究了一个完整的全纯矢量场在强伪凸复流形上的存在性,该流形具有负弯曲的完整Kähler-Einstein度量和一个离散的自同构序列。使用势能定标方法,我们将证明存在一个Kähler-Einstein度量的势函数,其微分具有恒定的长度。然后,我们将从势函数的梯度矢量场构造一个完整的全纯矢量场。