Diffeomorphisms between Siegel domains of the first kind preserving the holomorphic automorphism groups and applications

• Kodama Akio

  Faculty of Mathematics and Physics Institute of Science and Engineering Kanazawa University

• Shimizu Satoru

  Mathematical Institute Tohoku University

Abstract

This is a continuation of our previous paper [4]. In the class of hyperbolic manifolds in the sense of S. Kobayashi [3], we obtained in [4] an intrinsic characterization of bounded symmetric domains in Cⁿ from the viewpoint of the holomorphic automorphism group. In connection with this, we give in this paper a structure theorem on diffeomorphisms between Siegel domains of the first kind that preserve the holomorphic automorphism groups. As an application, we obtain a well-known fact [2] that two Siegel domains of the first kind are biholomorphically equivalent if and only if they are linearly equivalent.

Journal

• Kodai Mathematical Journal

  Kodai Mathematical Journal 36 (2), 299-312, 2013

  Department of Mathematics, Tokyo Institute of Technology

Keywords

• Holomorphic automorphism groups
• Siegel domains of the first kind
• Holomorphic equivalence problem

Details

• CRID: 1390001205272142336
• NII Article ID: 130004687987
• NII Article ID: 120005302283
• NII Book ID: AA00711773
• DOI: 10.2996/kmj/1372337520
• DOI: 10.24517/00010603
• ISSN: 18815472
• ISSN: 03865991
• MRID: 3081249
• Web Site: http://hdl.handle.net/2297/35100
• Text Lang: en
• Data Source:
  • JaLC
  • IRDB
  • Crossref
  • CiNii Articles
  • KAKEN
• Abstract License Flag: Disallowed