A study on characterization problems of complex manifolds by means of holomorphic automorphism groups

研究的主要目的是利用复流形的全纯自同构群的拓扑群结构来确定复流形的结构。这是非常困难的，目前还不能完全普遍地实现这一点。然而，我们可以得到有趣的结果出现在一些重要的模型空间的研究中的多个复变量。特别地，我们可以证明复欧氏空间中的有界对称域是由它们的全纯自同构群完全刻画的。

The main purpose of this research is to determine the complex manifold structure by means of the topological group structure of its holomorphic automorphism group. This is very difficult and this cannot be achieved in full generality at this moment. However, we could obtain interesting results on some important model spaces appearing in the study of several complex variables. Especially we could prove that bounded symmetric domains in the complex Euclidean space are completely characterized by their holomorphic automorphism groups.