On the Classification of Normal Stein Spaces and Finite Ball Quotients With Bergman–Einstein Metrics

Abstract We study the Bergman metric of a finite ball quotient $\mathbb{B}^n/\Gamma $, where $n \geq 2$ and $\Gamma \subseteq{\operatorname{Aut}}({\mathbb{B}}^n)$ is finite, fixed point free, abelian group. prove that this Kähler–Einstein if only $ trivial, is, when unit ${\mathbb{B}}^n$ itself. As consequence, we characterize among normal Stein spaces with isolated singularities fundamental groups in terms existence Bergman–Einstein metric.