Nearly Kähler 6-Manifolds with Reduced Holonomy

Florin Belgun (1) , Andrei Moroianu (2)

1 Institut für Mathematik [Berlin]
2 CMLS - Centre de Mathématiques Laurent Schwartz

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.

Mots clés: nearly Kähler manifolds; twistor spaces

Domaines: Géométrie différentielle [math.DG]

Florin Belgun, Andrei Moroianu. Nearly Kähler 6-Manifolds with Reduced Holonomy. Annals of Global Analysis and Geometry, 2001, 19, pp.307-319. ⟨10.1023/A:1010799215310⟩. ⟨hal-00125996⟩