A characterization of Ck x (C*) from the viewpoint of biholomorphic automorphism groups

Akio Kodama, Satoru Shimizu

Research output: Contribution to journalArticlepeer-review


We show that if a connected Stein manifold M of dimension n has the holomorphic automorphism group Aut(M) isomorphic to Aut(Ck x (C*)n-k) as topological groups, then M itself is biholomorphically equivalent to Ck x (C*)n-k. Besides, a new approach to the study of U(n)-actions on complex manifolds of dimension n is given.

Original languageEnglish
Pages (from-to)563-575
Number of pages13
JournalJournal of the Korean Mathematical Society
Issue number3
Publication statusPublished - 2003


  • Holomorphic automorphism groups
  • Holomorphic equivalences
  • Torus actions

ASJC Scopus subject areas

  • Mathematics(all)


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