On a Normal of the Distribution of Hyperplane Elements in an Affine Space

Abstract

Using the CartanLaptev invariant analytic method, an invariant affine normal (𝐸) is constructed, which is intrinsically connected with the distribution of hyperplane elements in the (𝑛 1)-dimensional affine space. For the normal (𝐸) we define a second kind normal and an invariant (𝑛 1)-dimensional plane lying in the plane of the element and not passing through the center and corresponding to this normal in the BompianiPantazi projectivity. An invariant point of intersection of the two-dimensional plane passing through the normals (𝐿) and (𝐸) with the second kind normal is found.