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 F_{1,2}={text {SU}}(3)/T^2 are not integrable into a curve of Einstein metrics.
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