Homogeneous Einstein metrics on Aloff-Wallach spaces (Q688084)

All homogeneous Einstein metrics on the (7-dimensional, compact) Aloff- Wallach spaces \(N_{k,\ell}\) are explicitly described. There are always two distinct homothety classes of such metrics. It is also proved that, for sufficiently large \(k\), the spaces \(N_{k,k+1}\) admit homogeneous Einstein metrics with positive sectional curvature.