Isometry groups of homogeneous quaternionic Kähler manifolds
type: Item
instance of: scholarly article
title: Isometry groups of homogeneous quaternionic Kähler manifolds
zbMATH Open document ID: 0973.53034
DOI: 10.1007/BF02921971
author: V. Cortés
author: Dmitri Alekseevsky
published in: The Journal of Geometric Analysis
publication date: 2000-12-11T00:00:00Z
review text: The authors present a general method for calculating the full isometry group of a Riemannian solvmanifold. They then use this method for calculating the full isometry group of the non-symmetric quaternionic Kähler solvmanifolds, that is, non-symmetric quaternionic Kähler manifolds admitting a transitive splittable solvable group of isometries. This is done explicitly and uses the classification of the quaternionic Kähler solvmanifolds. A remarkable consequence is that the connected component of the isometry group of a quaternionic Kähler solvmanifold acts transitively on the twistor space and on the \(\text{SO}_3\)-principal bundle associated with the quaternionic structure. Another consequence is that a quaternionic Kähler solvmanifold admits quotients of finite volume if and only if it is a symmetric space. Finally, they give a simple description of the quaternionic Kähler solvmanifolds in terms of certain spinorial modules of \(\text{Spin}(3,3+k)\).
reviewed by: Jürgen Berndt
Mathematics Subject Classification ID: 53C26
Mathematics Subject Classification ID: 53C28
Mathematics Subject Classification ID: 53C30
zbMATH DE Number: 1542113
zbMATH Keywords: Riemannian solvmanifold
zbMATH Keywords: isometry group
zbMATH Keywords: quaternionic Kähler solvmanifold
zbMATH Keywords: twistor space
zbMATH Keywords: quaternionic structure
zbMATH Keywords: quotients of finite volume
zbMATH Keywords: symmetric space
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1542113