On irreducible partials of Ricci tensor traceless part in finite space-time region in GR

Riemann tensor irreducible part $E_{iklm} = {1/2} (g_{il}S_{km} + g_{km}S_{il} - g_{im}S_{kl} - g_{kl}S_{im})$constructedfrommetrictensor$g_{ik}$andtracelesspartofRiccitensor$S_{ik} = R_{ik} - {1/4} g_{ik} R$ is expanded into bilinear combinations of bivectorial fields being eigenfunctions of $E$. Field equations for the bivectors induced by Bianchi identities are studied and it is shown that in general case it will be 3-parametric local symmetry group Yang-Mills field.