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

Akio Kodama, Satoru Shimizu

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish
Pages (from-to)299-312
Number of pages14
JournalKodai Mathematical Journal
Volume36
Issue number2
DOIs
Publication statusPublished - 2013

Keywords

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

ASJC Scopus subject areas

  • Mathematics(all)

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