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Sfb 288 Differential Geometry and Quantum Physics |
Abstract for Sfb Preprint No. 514
Hyper-Hermitian quaternionic Kaehler manifolds Bogdan Alexandrov
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.
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