Hyper-Hermitian Quaternionic Kähler Manifolds |
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Authors: | Bogdan Alexandrov |
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Institution: | (1) Institut für Mathemathik, Humboldt Universität zu Berlin, Rudower Chaussee 25, 10099 Berlin, Germany |
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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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Keywords: | quaternionic Kä hler manifold hyper-Hermitian structure Lee form |
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