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 P2m. We essentially use the hyperband distribution \( \mathcal{H} \) and P2m 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 \( \mathcal{M} \).