Abstract
The aim of this paper is to classify 4-dimensional Einstein-like manifolds whose Ricci tensor has constant eigenvalues (this being a special kind of curvature homogeneity condition). We give a full classification when the Ricci tensor is of Codazzi type; when the Ricci tensor is cyclic parallel, we classify all such manifolds when not all Ricci curvatures are distinct. In this second case we find a one-parameter family of Riemannian metrics on a Lie groupG as the only possible ones which are irreducible and non-symmetric.
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Podestà, F., Spiro, A. Four-dimensional Einstein-like manifolds and curvature homogeneity. Geom Dedicata 54, 225–243 (1995). https://doi.org/10.1007/BF01265339
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DOI: https://doi.org/10.1007/BF01265339