Hyper-Hermitian quaternionic Kaehler manifolds

2001/05/25 by Bogdan Alexandrov, Alexandrov, Bogdan
Mathematics · #53B35 #53C26 #Differential Geometry (math.DG) #FOS: Mathematics #math.DG #msc:53B35 #msc:53C26

paper · pdf · doi:10.48550/arxiv.math/0105206

21 pages, LATEX; several minor changes made

arxiv created 2001/10/30 · arxiv updated 2009/11/30

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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