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homogeneous Riemannian manifolds; Einstein manifolds; Ricci tensor; sectional curvature
We prove that there is exactly one homothety class of invariant Einstein metrics in each space $SU(2) \times SU(2) / SO(2)_r (r\in Q, \, |r|\neq 1)$ defined below.
[B] Besse A.: Einstein manifolds. Springer Verlag, Berlin, 1987. MR 0867684 | Zbl 1147.53001
[J] Jensen G.R.: Homogeneous Einstein spaces of dimension $4$. J. of Diff. Geom. 3 (1969), 309-349. MR 0261487
[K-V] Kowalski O., Vanhecke L.: Classification of five-dimensional naturally reductive spaces. Math. Proc. Camb. Phil. Soc. 97 (1985), 445-463. MR 0778679 | Zbl 0555.53024
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