论文标题
关于与伯格曼 - 因斯坦指标的普通斯坦（Stein）空间和有限球商的分类
On the classification of normal Stein spaces and finite ball quotients with Bergman-Einstein metrics
论文作者
论文摘要
在本文中，我们研究了有限的球商$ \ mathbb {b}^n/γ$的伯格曼度量，其中$γ\ subseteq \ subseteq \ mathrm {aut}（\ mathbb {b}^n）$是有限的，固定点免费，阿贝里安集团。我们证明，当$γ$是微不足道的情况下，即当球商$ \ mathbb {b}^n/γ$是单位球$ \ mathbb {b}^n $本身时，我们才证明该指标是Kähler-inenstein。结果，我们就伯格曼 - 因斯坦公制的存在，在具有孤立的奇异性和阿贝尔基本基团的正常施坦空间中建立了单位球的表征。
In this paper, we study the Bergman metric of a finite ball quotient $\mathbb{B}^n/Γ$, where $Γ\subseteq \mathrm{Aut}(\mathbb{B}^n)$ is a finite, fixed point free, abelian group. We prove that this metric is Kähler--Einstein if and only if $Γ$ is trivial, i.e., when the ball quotient $\mathbb{B}^n/Γ$ is the unit ball $\mathbb{B}^n$ itself. As a consequence, we establish a characterization of the unit ball among normal Stein spaces with isolated singularities and abelian fundamental groups in terms of the existence of a Bergman-Einstein metric.
