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Riemannian homogeneous manifold; Einstein manifold; weakly Einstein manifold

References:

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[2] Bergery, L. Bérard: **Four-dimensional homogeneous Riemannian spaces**. Riemannian Geometry in Dimension 4. Papers from the Arthur Besse seminar held at the Université de Paris VII, Paris, 1978/1979 L. Bérard Bergery et al. Mathematical Texts 3 CEDIC, Paris (1981), French. MR 0769130

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[8] Gray, A., Willmore, T. J.: **Mean-value theorems for Riemannian manifolds**. Proc. R. Soc. Edinb., Sect. A 92 (1982), 343-364. DOI 10.1017/S0308210500032571 | MR 0677493 | Zbl 0495.53040

[9] Jensen, G. R.: **Homogeneous Einstein spaces of dimension four**. J. Differ. Geom. 3 (1969), 309-349. MR 0261487 | Zbl 0194.53203

[10] Milnor, J. W.: **Curvatures of left invariant metrics on Lie groups**. Adv. Math. 21 (1976), 293-329. DOI 10.1016/S0001-8708(76)80002-3 | MR 0425012 | Zbl 0341.53030