Linear connections on the framed distribution of hyperplane elements in a conformal space

We study the geometry of affine and normal connections induced by a complete normalization of mutually orthogonal distributions $\mathcal M$ and $\mathcal H$ in conformal space $C_n$, where $\mathcal M$ is a distribution of hyperplane elements, and $\mathcal H$ is a distribution of line elements. We consider invariant fields of pencils that are parallel with respect to the normal connection $\overset{0}{\nabla}{}^\bot$ along any curve belonging to the distribution $\mathcal M$.