Invariant Einstein metrics on generalized flag manifolds of $Sp(n)$ and   $SO(2n)$
  It is well known that the Einstein equation on a Riemannian flag manifold $(G/K,g)$ reduces to an algebraic system if $g$ is a $G$-invariant metric. In this paper we obtain explicitly new invariant Einstein metrics on generalized flag manifolds of $Sp(n)$ and $SO(2n)$; and we compute the Einstein system for generalized flag manifolds of type $Sp(n)$. We also consider the isometric problem for these Einstein metrics. 
Luciana Aparecida Alves and Neiton Pereira da Silva
math.DG