2015 Issue №10

Construction of a general theory of a special class ( -distribution) of the regular threefold distributions ( -distribution [1]) of the projective space   consisting of a basic distribution of the 1st kind of r-dimensional planes   are equipped with the distribution of the 1st kind of m-dimensional planes   and equip distribution 1st the first kind of hyperplane elements (hyperplanes)   with the ratio of the incidence of the corresponding elements in the common center   is considered in this article. In this paper, these three distributions is considered as a immersed manifold. By virtue of the  -distribution structure in the geometry of the manifold are similar to some of the facts from the geometry of m-dimensional linear elements [2], (n-1)-dimensional linear elements [3]  and hyperband distribution [4]. However, the analogy does not relate to the geometry of the base only or equipping distributions taken separately.

A field of some geometrical objects internally connected with a complex (n-parametrical family) of the central nondegenerate hyperquadrics in n-dimensional affine space are defined and their geometrical sense is found out.

The vector field of the type  , obtained fr om the tensor field   on a smooth manifold M to the tangent bundle  , arises in the study of infinitesimal affine transformations with a complete lift. The H-lift was introduced S. Tanno in 1974 in infinitesimal isometries on the tangent bundle with the complete lift. The definition of H’-lift given by the author in this paper. There are established the properties of the entered lift and founded the commutator  , wh ere  .

The problem of constructing of center-projective group by factorization of the second order differential group is considered.