Hyper-Hermitian Quaternionic Kahler Manifolds

We call a quaternionic Kahler manifold with nonzero scalar curvature, whose quaternionic structure is trivialized by a hypercomplex structure, a hyper-Hermitian quaternionic Kahler manifold. We prove that every locally symmetric hyper-Hermitian quaternionic Kahler manifold is locally isometric to th...

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Bibliographic Details
Published in:Annals of global analysis and geometry 2002-08, Vol.22 (1), p.75
Main Author: Alexandrov, Bogdan
Format: Article
Language:English
Subjects:
Eigenvalues
Geometry
Mathematics
Theory
Online Access:Get full text
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Summary:We call a quaternionic Kahler manifold with nonzero scalar curvature, whose quaternionic structure is trivialized by a hypercomplex structure, a hyper-Hermitian quaternionic Kahler manifold. We prove that every locally symmetric hyper-Hermitian quaternionic Kahler manifold is locally isometric to the quaternionic projective space or to the quaternionic hyperbolic space. We describe locally the hyper-Hermitian quaternionic Kahler manifolds with closed Lee form and show that the only complete simply connected such manifold is the quaternionic hyperbolic space. [PUBLICATION ABSTRACT]
ISSN:0232-704X
1572-9060
DOI:10.1023/A:1016240817597