CSC Bergman metrics are Einstein on pseudoconvex domains

Abstract

Let $\Omega \subset {\mathbb{C}}^n$($n\ge 3$) be a pseudoconvex domain with a smooth strongly pseudoconvex boundary point. We prove that if the Bergman metric of $\Omega$ has constant scalar curvature, then it is necessarily Kähler--Einstein.

arXiv comment11 pages