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.
It is well known that the Einstein equation on a Riemannian flag manifold (G/K, g) reduces to a algebraic system, if g is a G-invariant metric. In this paper we described this system for all flag manifolds of a classical Lie group. We also determined the number of isotropy summands for all of these spaces and proved certain properties of the set of t-roots for flag manifolds of type Bn, Cn and Dn.
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