Invariant metrics and invariant functions on the Reinhardt domains
type: Item
instance of: scholarly article
title: Invariant metrics and invariant functions on the Reinhardt domains
zbMATH Open document ID: 0687.32020
author: Weiping Yin
published in: Chinese Science Bulletin
publication date: 1989-01-01T00:00:00Z
review text: This brief paper records several results, mostly without proofs. Consider the Reinhardt domain \[ D(K_ 1,...,K_ p)=\{z\in {\mathbb{C}}^ n| \quad \sum^{n}_{j=1}| z_ j|^{2K_ j}<1\} \] where \(K_ 1\geq...\geq K_ p>1\), \(K_{p+1}=...=K_ n=1\). When \(p=1\) write \(D(K_ 1)=D(K)\). The author lists the automorphisms of \(D(K_ 1,...,K_ p)\) in case \(K_ 1,...,K_ p\) are all different, and recalls a formula of D'Angelo for the Bergmann kernel function of D(K). The latter formula leads to the construction of a family of invariant Kähler metrics and of an invariant function on D(K). The author asks whether this invariant function generates all such functions.
Mathematics Subject Classification ID: 32A25
Mathematics Subject Classification ID: 32F45
Mathematics Subject Classification ID: 32A07
zbMATH DE Number: 4125792
zbMATH Keywords: invariant Kähler metric
zbMATH Keywords: Reinhardt domain
zbMATH Keywords: Bergmann kernel
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 4125792