Classification of invariant Einstein metrics on certain compact homogeneous spaces

Geodesic orbit metrics on homogeneous spaces constructed by strongly isotropy irreducible spaces

“…Remark 3.1. Here we get the classification directly from the group level, which is different from the classification given in [37] by Z. Yan, H. Chen and S. Deng. In fact, for any two different strongly isotropy irreducible spaces G i /K i (i = 1, 2) with the Lie algebras k i of K i (i = 1, 2) coincide, they got the classification of (g 1 ⊕ g 2 , ∆k), and then obtained the classification of (G 1 × G 2 )/ ∆K where ∆K is the connected Lie subgroup of G 1 × G 2 with the Lie algebra ∆k.…”