Any 6-dimensional strict nearly Kähler manifold is Einstein with positive scalar curvature. We compute the coindex of the metric with respect to the Einstein-Hilbert functional on each of the compact homogeneous examples. Moreover, we show that the infinitesimal Einstein deformations on F1,2=SU(3)/T2are not integrable into a curve of Einstein metrics.
We prove the linear stability with respect to the Einstein-Hilbert action of the symmetric spaces SU(n), n≥3, and E6/F4. Combined with earlier results, this resolves the stability problem for irreducible symmetric spaces of compact type.
