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Summary:
The author obtains the classification of all invariant Einstein metrics on the following homogeneous spaces: $SU(3)/T\sb{\max}$, $Sp(3)/Sp(1) \times Sp(1) \times Sp(1)$, $F\sb 4/ \text {spin} (8)$, $SU(5)/Sp(2) \times T\sp 1$. Combining this with the results of other authors, the classification of all invariant Einstein metrics on all compact simply connected homogeneous spaces admitting a homogeneous Riemannian metric of positive sectional curvature is obtained.
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