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

Kodai Mathematical Journal

Akio Kodama¹  Satoru Shimizu² 

[1] Faculty of Mathematics and Physics Institute of Science and Engineering Kanazawa University;Mathematical Institute Tohoku University

关键词: Holomorphic automorphism groups;    Siegel domains of the first kind;    Holomorphic equivalence problem;   

DOI  :  10.2996/kmj/1372337520

学科分类：数学（综合）

来源: Tokyo Institute of Technology, Department of Mathematics

【 摘 要 】

References(9)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.

【 授权许可】

Unknown