The Einstein-Kähler metric on \(\{| z| ^ 2+| w| ^{2p}<1\}\)
type: Item
instance of: scholarly article
title: The Einstein-Kähler metric on \(\{| z| ^ 2+| w| ^{2p}<1\}\)
zbMATH Open document ID: 0602.32005
author: John S. Bland
published in: Michigan Mathematical Journal
publication date: 1986-01-01T00:00:00Z
review text: The aim of the paper is to describe the Einstein-Kähler metric for the domain \(D = \{(z,w)\in {\mathbb{C}}^ n\times {\mathbb{C}}: \| z\|^ 2 + | w|^{2p}< 1\}\) where p is a positive number. A formula for the metric is given in terms of a function determined by a differential equation. Moreover, the components of the curvature tensor for the metric are calculated and the behaviour of the metric near boundary points of special interest is analyzed. (The existence of Einstein-Kähler metrics in bounded pseudoconvex domains has been proved by \textit{N. Mok} and \textit{S. T. Yau} in Proc. Symp. Pure Math. 39, Part 1, 41-59 (1983; Zbl 0526.53056). The case of bounded pseudoconvex domains with \({\mathcal C}^ 2\)-boundary has been investigated by \textit{S. Y. Cheng} and \textit{S. T. Yau} in Commun. Pure Appl. Math. 33, 507-544 (1980; Zbl 0506.53031).)
Mathematics Subject Classification ID: 32T99
Mathematics Subject Classification ID: 32M99
Mathematics Subject Classification ID: 53C55
Mathematics Subject Classification ID: 53B35
zbMATH DE Number: 3971183
zbMATH Keywords: boundary behaviour
zbMATH Keywords: curvature tensor
zbMATH Keywords: Einstein-Kähler metrics in bounded pseudoconvex domains
reviewed by: M. Klimek
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1307/mmj/1029003350
OpenAlex ID: W2083924764
DOI: 10.1307/MMJ/1029003350
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description: scientific article; zbMATH DE number 3971183