Dual geometry of Cartan distribution

Abstract

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 $\mathcal{M}$.