Eteri Alshibaia

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

Using the Cartan-Laptev 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 Bompiani-Pantazi 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. The construction is carried out without assuming that the nonholonomy tensor is different from zero. Hence both nonholonomic and holonomic distributions are framed by the constructed normal.

Fibre space, hyperplane element, holonomic and nonholonomic distributions, differential continuation, affine normal, fundamental object.

MSC 2000: 53A15