摘要：Sufficient conditions on a pseudoprojective symmetric spacetime PPSn whose Ricci tensor is of Codazzi type to be either a perfect fluid or Einstein spacetime are given. Also, it is shown that a PPSn is Einstein if its Ricci tensor is cyclic parallel. Next, we illustrate that a conformally flat PPSn spacetime is of constant curvature. Finally, we investigate conformally flat PPS4 spacetimes and conformally flat PPS4 perfect fluids in fR,G theory of gravity, and amongst many results, it is proved that the isotropic pressure and the energy density of conformally flat perfect fluid PPS4 spacetimes are constants and such perfect fluid behaves like a cosmological constant. Further, in this setting, we consider some energy conditions.
