一类三维圆柱域的交点域与复欧氏空间的公共子流形

Common submanifolds of the intersection of cylindrical field and complex Euclidean spaces

摘要: 两个圆柱域的交点域 Bergman 核函数具有显表达式。在三维情况下，其Bergman核函数不再是有理函数。证明了在三维情况下具有Bergman度量的两个圆柱域的交点域与具有平坦度量的复欧氏空间不存在公共的Kähler子流形。

Abstract: The Bergman kernel function of the intersection of two cylindrical domains has an explicit form. In three-dimensional case， the Bergman kernel is not a rational function. It was proved that there was no common Kähler submanifold between the intersection of two cylindrical domains with Bergman metric and the complex Euclidean space with flat metric.