On the convexity of the Kobayashi metric on a taut complex manifold
type: Item
instance of: scholarly article
title: On the convexity of the Kobayashi metric on a taut complex manifold
zbMATH Open document ID: 1020.32007
author: Masashi Kobayashi
published in: Pacific Journal of Mathematics
publication date: 2000-12-03T00:00:00Z
review text: Let \(M\) be an \(m\)-dimensional complex manifold, and \(F_M\) be the Kobayashi-Royden pseudo-metric on \(M\). \(F_M\) induces a pseudo-distance \(d_M\), which is called the Kobayashi pseudo-distance. \textit{S. Kobayashi} recently introduced [Int. J. Math. 1, 83-90 (1990; Zbl 0702.32021)] a new infinitesimal pseudo-metric \({\hat F}_M\) on \(M\) which is the double dual of \(F_M\). This paper proves that, if \(M\) is a taut complex manifold, then \({\mathcal D}d_M\) exists, and \({\mathcal D}d_M={\hat F}_M\), where \({\mathcal D}d_M\) is the \textit{derivative} of \(d_M\) (see the paper for the precise definition).
reviewed by: Min Ru
Mathematics Subject Classification ID: 32F45
Mathematics Subject Classification ID: 32Q45
zbMATH DE Number: 1537830
zbMATH Keywords: Kobayahsi pseudo-distance
zbMATH Keywords: taut complex manifold
zbMATH Keywords: Kobayashi-Royden pseudometric
MaRDI profile type: Publication
full work available at URL: pjm.2000.194.117
OpenAlex ID: W1978870968
DOI: 10.2140/PJM.2000.194.117
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description: scientific article; zbMATH DE number 1537830