酉群对Hopf流形的直子的有效传递作用
Effective transitive actions of the unitary group on quotients of Hopf manifolds
摘要：
在2002年的文章中，我们与N. Kruzhilin我们证明了，每个连通复流形的尺寸$n\ge 2$，承认一个有效的传递作用的酉群${\rm U}_n$是双全纯的商的Hopf流形的作用${\mathbb Z}_m$为一些整数$m$满足$(n,m)=1$。在这篇文章中，我们补充了上述结果，明确描述了${\rm U}_n$对这些事件的所有有效传递作用，这为一个10年前的问题提供了答案。
英文摘要：
In our article of 2002 joint with N. Kruzhilin we showed that every connected complex manifold of dimension $n\ge 2$ that admits an effective transitive action by holomorphic transformations of the unitary group ${\rm U}_n$ is biholomorphic to the quotient of a Hopf manifold by the action of ${\mathbb Z}_m$ for some integer $m$ satisfying $(n,m)=1$. In this note, we complement the above result with an explicit description of all effective transitive actions of ${\rm U}_n$ on such quotients, which provides an answer to a 10-year old question.
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