发表机构
Northwest University; Henan Normal University; Capital Normal University（西北大学; 河南师范大学; 首都师范大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文计算了完备Kähler-Einstein流形上圆盘丛的完备Kähler-Einstein度量的截面曲率，并研究其负夹挤性；对伪凸Hartogs域，证明了Bergman度量为Kähler-Einstein当且仅当域双全纯等价于单位球。
AI 中文摘要
本文计算了任意完备Kähler-Einstein流形上的圆盘丛所配备的完备Kähler-Einstein度量的全纯截面曲率和黎曼截面曲率。随后我们研究该度量是否为负定夹挤的。当底空间为带有其完备Kähler-Einstein度量的有界伪凸域时，相应的圆盘丛是一个伪凸Hartogs域。我们证明了此类Hartogs域上的Bergman度量是Kähler-Einstein的，当且仅当该域双全纯等价于单位球。
英文摘要
In this paper, we study some geometric properties of the disk bundles over the complete Kähler manifolds. When the base space is the complete Kähler-Einstein manifold, we compute the holomorphic sectional curvature, Riemannian sectional curvature of the complete Kähler-Einstein metric on the disk bundle. Moreover, we present a parametric criteria for whether the manifold admits negative pinched property. When the base space is a bounded pseudoconvex domain equipped with its complete Kähler metric, the corresponding ball bundle in the $k$-direct sum of line bundles is a bounded pseudoconvex Hartogs domain with fiber dimension $k$ . If the base domain is simply-connected and $k\geq2$, we prove that the Bergman metric on such a Hartogs domain is Kähler-Einstein if and only if the domain is biholomorphically equivalent to a unit ball.
