Nearly Kähler 6-Manifolds with Reduced Holonomy

Abstract : We consider a complete six-dimensional nearly Kähler manifold together with the first canonical Hermitian connection. We show that if the holonomy of this connection is reducible, then the manifold endowed with a modified metric and almost complex structure is a Kählerian twistor space. This result was conjectured by Reyes-Carrión.
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Florin Belgun, Andrei Moroianu. Nearly Kähler 6-Manifolds with Reduced Holonomy. Annals of Global Analysis and Geometry, Springer Verlag, 2001, 19, pp.307-319. ⟨10.1023/A:1010799215310⟩. ⟨hal-00125996⟩

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