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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Published in:Annals of global analysis and geometry 2002-08, Vol.22 (1), p.75
Main Author: Alexandrov, Bogdan
Format: Article
Language:English
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Eigenvalues
Geometry
Mathematics
Theory
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description 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]
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subjects Eigenvalues
Geometry
Mathematics
Theory
title Hyper-Hermitian Quaternionic Kahler Manifolds
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