Spectral properties of the twistor fibration of a quaternion Kähler manifold
type: Item
instance of: scholarly article
title: Spectral properties of the twistor fibration of a quaternion Kähler manifold
zbMATH Open document ID: 0968.53034
DOI: 10.1016/S0021-7824(00)00145-8
published in: Journal de Mathématiques Pures et Appliquées. Neuvième Série
publication date: 2000-06-22T00:00:00Z
review text: The authors investigate relations between Killing vector fields and eigenforms of the Laplacian on a quaternion-Kähler manifold \(M\) using spectral properties of the Kähler-Einstein twistor space \(Z\). It is shown that the Hamiltonian of a Killing field is an eigenform of the Laplacian corresponding to a minimal non-zero eigenvalue. This result gives a quaternionic version of a famous result of Lichnerowicz and Matsushima on Kähler-Einstein geometry. Using the twistor fibration \(t: Z\to M\) some relations between the spectral geometries of \(Z\) and \(M\) are established.
Mathematics Subject Classification ID: 53C28
Mathematics Subject Classification ID: 53C26
zbMATH DE Number: 1463864
zbMATH Keywords: Hamiltonian form
zbMATH Keywords: Killing vector field
zbMATH Keywords: quaternion-Kähler manifold
zbMATH Keywords: eigenform of the Laplacian
zbMATH Keywords: twistor fibration
author: Dmitri Alekseevsky
author: S. Marchiafava
author: Massimiliano Pontecorvo
reviewed by: Marian Ioan Munteanu
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1463864