Hyper-Hermitian quaternionic Kaehler manifolds

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We call a quaternionic Kaehler manifold with non-zero scalar curvature, whose quaternionic structure is trivialized by a hypercomplex structure, a hyper-Hermitian quaternionic Kaehler manifold. We prove that every locally symmetric hyper-Hermitian quaternionic Kaehler manifold is locally isometric to the quaternionic projective space or to the quaternionic hyperbolic space. We describe locally the hyper-Hermitian quaternionic Kaehler manifolds with closed Lee form and show that the only complete simply connected such manifold is the quaternionic hyperbolic space.
21 pages, LATEX; several minor changes made

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Differential Geometry, 53B35;53C26

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http://salesiana.dossiersoluciones.com/handle/123456789/61529

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0105206
 http://arxiv.org/abs/math/0105206

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arXiv