Hyper-Hermitian quaternionic Kaehler manifolds

Bogdan Alexandrov

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Hyper-Hermitian quaternionic Kaehler manifolds

Bogdan Alexandrov

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Abstract

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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Bogdan Alexandrov. 2001-10-30. Hyper-Hermitian quaternionic Kaehler manifolds. https://arxiv.org/abs/math/0105206

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