Two Kähler manifolds are called relatives if they admit a common Kähler submanifold with their induced metrics. In this paper, we provide a sufficient condition to determine whether a real analytic Kähler manifold is not a relative to a complex space form equipped with its canonical metric. As an application, we show that minimal domains, bounded homogeneous domains and some Hartogs domains equipped with their Bergman metrics are not relatives to the complex Euclidean space.

中文翻译：

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关于Kähler流形和复杂空间形式的公共子流形的不存在

如果两个Kähler流形接受其诱导度量的公共Kähler子流形，则称为亲属。在本文中，我们提供了充分的条件来确定实际的解析Kähler流形是否不是相对于配备其规范度量的复杂空间形式的。作为一个应用程序，我们表明最小域，有界齐次域和配备其Bergman度量的某些Hartogs域不是相对于复杂的欧几里得空间的。