This is a continuation of our previous paper . In the class of hyperbolic manifolds in the sense of S. Kobayashi , we obtained in  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  that two Siegel domains of the first kind are biholomorphically equivalent if and only if they are linearly equivalent.
- Holomorphic automorphism groups
- Holomorphic equivalence problem
- Siegel domains of the first kind
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