Some Other Invariant Metrics

Abstract

Chapters 3 and 4 explored extensively the use of the Bergman metric in studying the function theory of bounded domains and in particular their automorphism groups. The Bergman metric also played a role in Chapter 5 in the Bedford/Dadok proof of the realizability of every compact Lie group as an automorphism group. In all these instances, the invariance of the Bergman metric made it possible to bring to bear powerful differential geometric methods that would not have been otherwise available. But there are other invariant metrics that also deserve attention for their utility in such investigations. The purpose of this chapter is to give a quick survey of some of them.