New Einstein-Randers metrics on some homogeneous manifolds

In this article, we find several new non-Riemannian Einstein-Randes metrics on some homogeneous manifolds arising from the exceptional Lie groups. Based on the discussions about generalized flag manifolds with second Betti number b(2)(M) = 1, we firstly prove that there exists Riemannian Einstein metrics on these homogeneous manifolds. Then, we prove that there exists non-Riemannian Einstein-Randers metrics on these homogeneous manifolds.