On a class of solvable Kähler algebras of nonpositive curvature
type: Item
instance of: scholarly article
title: On a class of solvable Kähler algebras of nonpositive curvature
zbMATH Open document ID: 0930.53034
DOI: 10.1023/A:1004964418037
author: Maria J. Druetta
published in: Geometriae Dedicata
publication date: 2000-02-15T00:00:00Z
review text: The authors study the class of solvable Kähler algebras associated to simply connected solvable Lie groups with left invariant Kähler metrics of non-positive, sectional or holomorphic curvature, and without flat de Rham factor. In Section 2 it is shown, using modifications, that this class is in one to one correspondence with normal \(j\)-algebras of non-positive, either sectional or holomorphic curvature. Sections 3 and 4 are devoted to the classification of the above class of Kähler algebras in dimension 6. In Theorem 3.3, a one parameter family of Kähler metrics \(\langle , \rangle_t\) of non-positive sectional or holomorphic curvature on a solvable Lie group \(S\) is given; the metric is symmetric for one fixed \(t\) and different values of \(t\) give rise to non-isometric Riemannian manifolds (see Proposition 3.5). In Theorem 4.1, the full classification of simply connected homogeneous Kähler manifolds of dimension 6 without flat de Rham factor, admitting a simply transitive solvable Lie group of holomorphic isometries and having non-positive, either sectional or holomorphic curvature, is given. The resulting Riemannian manifolds are symmetric with the exception of the one parameter group considered in Theorem 3.3.
Mathematics Subject Classification ID: 53C30
Mathematics Subject Classification ID: 53C55
zbMATH DE Number: 1003884
zbMATH Keywords: non-positive curvature
zbMATH Keywords: sectional curvature
zbMATH Keywords: Kähler algebras
zbMATH Keywords: homogeneous Kähler manifolds
zbMATH Keywords: holomorphic curvature
reviewed by: Isabel Dotti Miatello
MaRDI profile type: Publication
full work available at URL: a:1004964418037
OpenAlex ID: W2913359562
description: scientific article; zbMATH DE number 1003884