Intrinsic normalization of a hyperplane distribution on the Grassmann manifold. I (Q1568070)

In this note, the author considers the constructions of intrinsic normalizations in the sense of E. Cartan and in the sense of Bortolotti for a distribution of hyperplanes \(\omega_{\alpha}^{n+1}=\lambda_{\alpha \beta}^{p} \omega_{p}^{\beta} +\lambda_{\alpha}^{p} \cdot \omega_{p}^{n+1}\) on the Grassmann manifold \(Gr(m,n)\) of \(m\)-dimensional planes \(l_{m}\) of the \(n\)-dimensional projective space \(P_{n}\), each hyperplane of which passes through the corresponding \(m\)-plane.