Hyper-Hermitian quaternionic Kaehler manifolds

Details Hyper-Hermitian quaternionic Kaehler manifolds Hyper-Hermitian quaternionic Kaehler manifolds

2001-05-25

arxiv.org/abs/math/0105206v3

Mathematics

Differential Geometry

21 pages, LATEX; several minor changes made

Scientific paper

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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