The dual geometry of the Cartan distribution

The paper is devoted to the study of intrinsic geometry of a Cartan distribution $\mathcal M$ in projective space $\mathrm{P}_{2m}$. We essentially use the hyperband distribution $\mathcal H$ in $\mathrm P_{2m}$ associated with $\mathcal M$. Using the duality theory, we construct, in the 4th differential neighborhood, a series of normalizations of $\mathcal M$. We also consider dual affine connections $\overset{1}{\nabla}$ and $\overset{2}{\nabla}$ induced by the dual normalization of the Cartan distribution $\mathcal M$.