Homogeneous nearly Kähler manifolds

Abstract

The structure of nearly Kähler manifolds was studied by Gray in several papers. More recently, a relevant progress on the subject has been done by Nagy. Among other results, he proved that a strict and complete nearly Kähler manifold is locally a Riemannian product of homogeneous nearly Kähler spaces, twistor spaces over quaternionic K{ähler manifolds and six-dimensional nearly Kähler manifolds, where the homogeneous nearly Kähler factors are also 3-symmetric spaces. In the present paper, using the lists of $3$-symmetric spaces given by Wolf & Gray, we display the exhaustive list of irreducible simply connected homogeneous strict nearly Kähler manifolds. For such manifolds, we give details relative to the intrinsic torsion and the Riemannian curvature. Additionally, we determine the canonical fibration for those with special algebraic torsion.

42 pages