The subject of the paper is a self-recurrent $SW-O_n$ and its covariantly geodesic lines; first, conditions are found for such a $SW-O_n$ to be $\pi$-projective to its own adjoint Riemannian space; then, conditions are found for two self-recurrent $SW-O_ns$ to be covariantly projective, that is, to have covariantly geodesic lines in common; third, it is proved that two different $SW-0_ns$ over the same Riemannian space cannot be $\pi$-projective.