Abstract
We call a quaternionic Kähler manifold with nonzero scalar curvature, whosequaternionic structure is trivialized by a hypercomplex structure, ahyper-Hermitian quaternionic Kähler manifold. We prove that every locallysymmetric hyper-Hermitian quaternionic Kähler manifold is locally isometricto the quaternionic projective space or to the quaternionic hyperbolic space.We describe locally the hyper-Hermitian quaternionic Kähler manifolds withclosed Lee form and show that the only complete simply connected suchmanifold is the quaternionic hyperbolic space.
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Alexandrov, B. Hyper-Hermitian Quaternionic Kähler Manifolds. Annals of Global Analysis and Geometry 22, 75–98 (2002). https://doi.org/10.1023/A:1016240817597
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DOI: https://doi.org/10.1023/A:1016240817597