The intrinsic metrics on the circular domains in \({\mathbb{C}}^ n\)
type: Item
instance of: scholarly article
title: The intrinsic metrics on the circular domains in \({\mathbb{C}}^ n\)
zbMATH Open document ID: 0535.32014
author: Masaaki Suzuki
published in: Pacific Journal of Mathematics
publication date: 1984-01-01T00:00:00Z
review text: In this paper the intrinsic metrics on the circular domains in \({\mathbb{C}}^ n\) are studied. Using the results of \textit{A. Sadullaev} [Math. Notes 27, 120-125 (1980); translation from Mat. Zametki 27, 245- 253 (1980; Zbl 0431.32018)], the author calculates the Kobayashi metric at the center of a pseudoconvex complete (bounded) circular domain D. Moreover, if D is convex then the Caratheodory and Kobayashi metric coincide at the center of D. \textit{T. J. Barth} [Proc. Am. Math. Soc. 88, 527-530 (1983; Zbl 0494.32008)] has obtained the same results by a different method. In the final section the author explicitly gives the intrinsic metrics for Cartan's classical domains. For this, see the author, Math. Rep., Toyama Univ. 6, 143-177 (1983; Zbl 0522.32020).
Mathematics Subject Classification ID: 32F45
Mathematics Subject Classification ID: 32M15
zbMATH DE Number: 3849609
zbMATH Keywords: Caratheodory metric
zbMATH Keywords: classical Cartan domain
zbMATH Keywords: circular domains
zbMATH Keywords: Kobayashi metric
MaRDI profile type: Publication
full work available at URL: pjm.1984.112.249
OpenAlex ID: W2013809026
DOI: 10.2140/PJM.1984.112.249
description: scientific article; zbMATH DE number 3849609