Automorphisms of certain Stein manifolds
type: Item
instance of: scholarly article
title: Automorphisms of certain Stein manifolds
zbMATH Open document ID: 0829.32009
DOI: 10.1007/BF02572371
author: Róbert Szőke
published in: Mathematische Zeitschrift
publication date: 1996-01-28T00:00:00Z
full work available at URL: https://eudml.org/doc/174779
review text: Let \((M,g)\) be a compact, real analytic Riemannian manifold. Let \(0<r\leq\infty\). Denote by \(T^rM\) the disk bundle over \(M\) that consists of all the tangent vectors having \(g\)-length smaller than \(r\). For a given \((M,g)\) there exists an \(r\) and a canonically defined (adapted to the metric \(g\)) complex manifold structure \(J_g\) on \(T^rM\). The \(g\)-norm square function \(\rho\) is strictly plurisubharmonic with respect to \(J_g\), hence \((T^rM,J_g)\) is a Stein manifold. Denote by \(\kappa_g\) the Kähler metric on \(T^rM\) induced by \(\rho\). The main purpose of this paper is to study biholomorphic maps between and automorphisms of this type of Stein manifolds. We also discuss the question when such a biholomorphism is an isometry with respect to \(\kappa_g\).
Mathematics Subject Classification ID: 32E10
Mathematics Subject Classification ID: 32W20
Mathematics Subject Classification ID: 32H02
Mathematics Subject Classification ID: 32Q45
Mathematics Subject Classification ID: 53C55
zbMATH DE Number: 795027
zbMATH Keywords: biholomorphic maps
zbMATH Keywords: automorphisms
zbMATH Keywords: Stein manifolds
zbMATH Keywords: isometry
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 795027