Abstract
We construct the Einstein equation for an invariant Riemannian metric on generalized flag manifolds G/K with G2-type t-roots. By computing a Gršobner basis for a system of polynomials on six variables, we prove that such a generalized flag manifold G/K, which is not the full flag manifold G2/T, admits exactly one invariant Kahler Einstein metric and six non Kahler invariant Einstein metrics up to isometry and scalar.
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