Nearly Kähler 6-Manifolds with Reduced Holonomy

By F. Belgun, Andrei Moroianu. 2001

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Maximally homogeneous para-CR manifolds of semisimple type (2006, unknown): “er manifold. Then ∇ψ± = 0 in other words the Nijenhuis tensor of J is parallel w.r.t the canonical Hermitian connection. This has been proved ﬁrst by Kirichenko [43] and a short proof can be found in [5]. It also follows from our Theorem 3.1, which is unifying this type of property in the class G1. ”
Almost parallel structures (2001, background): “Any 6-dimensional strictly nearlyKähler manifold has a canonical connection with holonomy SU(3), and this reduces to U(2) if and only if M fibres over a self-dual Einstein 4-manifold (Belgun and Morioanu, 2000).”
Homogeneous nearly K\"{a}hler manifolds (2006, background): “Next, in the 70’s [22, 25] and more recently (we mention, as a very incomplete list of references on the topic: [38, 6, 35] and [36]), nearly Khler manifolds have been studied for themselves.”
Nearly Kaehler geometry and Riemannian foliations (2002, background): “We recall now that ∇(∇J) = 0, a fact proven in [1], which is equivalent to”
On Nearly-Kähler Geometry (2002, methodology): “2 was already proven in 6-dimensions by a different method in [2].”