Investigation of all Ricci semi-symmetric and all conformally semi-symmetric spacetimes

We find all Ricci semi-symmetric as well as all conformally semi-symmetric spacetimes. Neither of these properties implies the other. However, we find that for spacetimes (3+1 dim) with nonzero Weyl tensor and nonzero tracefree part of the Ricci tensor conformal semi-symmetry and Ricci semi-symmetry is equivalent.