Coindex and rigidity of Einstein metrics on homogeneous Gray manifolds

Abstract

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.