Complex geodesics and holomorphic retracts of dimension 1
type: Item
instance of: scholarly article
title: Complex geodesics and holomorphic retracts of dimension 1
zbMATH Open document ID: 0960.32012
DOI: 10.1007/BF02505991
published in: Annali di Matematica Pura ed Applicata. Serie Quarta
publication date: 2001-05-17T00:00:00Z
review text: Let \(D\) be a bounded domain in \(\mathbb{C}^n\) and \(V\) an analytic subvariety of \(D\). In the case where \(V\) is biholomorphically equivalent to the unit disc in \(\mathbb{C}\), \textit{L. Lempert} gave a characterization of complex geodesics by holomorphic retraction [Anal. Math. 8, 257-261 (1982; Zbl 0509.32015)]. After the study of Lempert, the author deals with the case where \(V\) is a hyperbolic subvariety of dimension 1. To this end, he defines new invariant metrics, one is of Carathéodory type and another one is of Kobayashi type. He proves two fundamental results similar to the theorem of Lempert. He gives calculations of the above pseudometrics in a certain simple case and its application.
reviewed by: Yoshihiro Aihara
Mathematics Subject Classification ID: 32F45
Mathematics Subject Classification ID: 32Q45
zbMATH DE Number: 1472033
zbMATH Keywords: invariant distance
zbMATH Keywords: complex geodesics
zbMATH Keywords: holomorphic retraction
author: Jean-Pierre Vigué
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1472033