Hyperbolic \(n\)-dimensional manifolds with automorphism group of dimension \(n^2\)
type: Item
instance of: scholarly article
title: Hyperbolic \(n\)-dimensional manifolds with automorphism group of dimension \(n^2\)
zbMATH Open document ID: 1120.32014
published in: Geometric and Functional Analysis. GAFA
publication date: 2007-05-14T00:00:00Z
review text: Let \(M\) be a connected complex manifold of dimension \(n\) and denote by \(\Aut(M)\) the group of holomorphic automorphisms of \(M\). If \(M\) is Kobayashi hyperbolic then \(\Aut(M)\) carries the structure of a Lie group. It is known that \(d(M)\), the dimension of \(\Aut(M)\) is upper bounded by \(n^2+2n\) with equality if and only if \(M\) is holomorphically equivalent to the unit ball. \(M\) is homogeneous whenever \(d(M)> n^2\). If \(d(M)=n^2\) then \(M\) need not to be homogeneous, futher not all hyperbolic manifolds with \(d(M)=n^2\) are complete and simply connected. In this paper the author classifies connected hyperbolic manifolds of dimension \(n\geq 2\) greater or equal two with \(d(M))=n^2\) (up to holomorphic equivalence). In the proof, one can find the respective automorphism group.
Mathematics Subject Classification ID: 32Q45
Mathematics Subject Classification ID: 32M05
Mathematics Subject Classification ID: 32M10
zbMATH DE Number: 5152560
zbMATH Keywords: complex Kobayashi hyperbolic manifolds
zbMATH Keywords: holomorphic automorphism group
author: A. V. Isaev
reviewed by: Gabriela Paola Ovando
MaRDI profile type: Publication
full work available at URL: s00039-006-0586-3
OpenAlex ID: W2896897973
Wikidata QID: Q125870134
DOI: 10.1007/S00039-006-0586-3
description: scientific article; zbMATH DE number 5152560