Distributions of tangent elements

An $n$-dimensional differentiable manifold is considered, on which a Lie group operates.
As an example, we can take point projective space or line projective space and the projective group operating on it etc.
Any $m$-dimensional submanifold containing a fixed element of the manifold generates a geometric object (fundamental object of the first order), which we call an $m$-dlmensional tangent element.
Thus a fibre bundle of $m$-dimensional tangent elements is defined; a cross section of this fibre bundle is called a non-holonomic manifold or a distribution.
The system of differential equations of the distribution written in invariant form (3.3) generates a sequence of fundamental geometrical objects which are used to construct the differential geometry of distribution.
A system (5.2) of differential equations (the associated system of the distribution) is introduced. An invariant condition of holonomity of the distribution is given. For a holonomic distribution the associated system is completely integrable and defines a $(n-m)$-parametric family of $m$-dimensional subrnanifolds envelopped by the elements of the distribution.
In general case the class of curves (curves belonging to the distribution) is invariantly characterized; these curves are the 1-dimensional integral varieties of the associated system.
In § 8 the distributions of tangent elements are considered in spaces with connection and arbitrary generating element.