Effective Transitive Actions of the Unitary Group on Quotients of Hopf Manifolds

Abstract

In our joint article with N. Kruzhilin of 2002, we showed that every connected complex manifold of dimension n ≥ 2 that admits an effective transitive action by holomorphic transformations of the unitary group Un is biholomorphic to the quotient of a Hopf manifold by the action of Zm 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 Un on such quotients, which provides an answer to a 10-year-old question.