Non-Riemannian Einstein-Randers metrics on $E_6/A_4$ and $E_6/A_1$

In this paper, we first prove that homogeneous spaces $E_6/A_4$ and $E_6/A_1$ admit Einstein metrics which are $Ad(Ttimes A_1times A_4)$-invariant, and then show that they admit Non-Riemannian Einstein-Randers metrics.