The isometry groups of manifolds and the automorphism groups of domains

Abstract

ABSTRACT. We prove that every compact Lie group can be realized as the (full) automorphism group of a strictly pseudoconvex domain and as the (full) isometry group of a compact, connected, smooth Riemannian manifold.

Some aspects of holomorphic mappings: A survey

“…Note that any compact real Lie group can be realized as an automorphism group of a strictly pseudoconvex domain [15,134]. 7.2.…”

On automorphism groups of generalized Hua domains

“…From the work of Bedford-Dadok [2] and Saerens-Zame [13], it is known that every compact Lie group can be realized as the automorphism group of a strictly pseudoconvex bounded domain with real analytic boundary in C N . On the other hand, from the work of B. Wong [15], a C ∞ strongly pseudoconvex domain with a noncompact automorphism group is necessarily biholomorphic to the unit ball.…”

Domains with Prescribed Automorphism Group

“…Thus, it makes sense to say that most strictly pseudoconvex bounded domains possess compact automorphism group. Indeed, it has been proved, by Bedford-Dadok [1] and Saerens-Zame [14] in 1987, that any compact Lie group can be realized as the automorphism group of a strictly pseudoconvex domain.…”

“…Naturally both [1] and [14] and the methods therein should be relevant to our work, whereas the two papers are quite different in their methods. In this article we choose to follow the circle of ideas in [14].…”

“…In this article we choose to follow the circle of ideas in [14]. In Appendix, we recapitulate the main contents of the paper [14] of Saerens and Zame due to two reasons: (1) Their arguments play an important role in this article, and (2) Some of their reasonings seem problematic and hence needs adjustments.…”