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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. Inthis paper we described this system for all flag manifolds of a classical Liegroup. We also determined the number of isotropy summands for all of thesespaces and proved certain properties of the set of t-roots for flag manifoldsof type $B_n$, $C_n$ and $D_n$.

Isotropy summands and Einstein Equation of Invariant Metrics on Classical Flag Manifolds