On nearly Kaehler geometry

2001/10/05 by Paul-Andi Nagy, Nagy, Paul-Andi
Mathematics · #53C12 #53C24 #53C29 #5C28 #Differential Geometry (math.DG) #FOS: Mathematics #math.DG #msc:53C12 #msc:53C24 #msc:53C29 #msc:5C28

paper · pdf · doi:10.48550/arxiv.math/0110065

10 pages

arxiv created 2001/10/05 · arxiv updated 2009/11/30

Abstract

We consider complete nearly Kähler manifolds with the canonical Hermitian connection. We prove some metric properties of strict nearly Kähler manifolds and give a sufficient condition for the reducibility of the canonical Hermitian connection. A holonomic condition for a nearly Kähler manifold to be a twistor space over a quaternionic Kähler manifold is given. This enables us to give classification results in 10-dimensions.

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