Dual geometry of Cartan distribution

The paper is devoted to the study of intrinsic geometry of a Cartan distribution (mathcal{M}) in projective space P_2m . We essentially use the hyperband distribution (mathcal{H}) and 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 (mathop nabla limits^1 ) and (mathop nabla limits^2 ) induced by the dual normalization of the Cartan distribution (mathcal{M}).