  The article consists of the Russian and English variants of Ph.D. Thesis in
which the answers is given on the following questions:
  1. how to construct the spinor formalism for n=6;
  2. how to construct the spinor formalism for n=8;
  3. how to prolong the Riemannian connection from the tangent bundle into the
spinor one with the base: a complex analytical 6-dimensional Riemannian space;
  4. how to construct the real and complex representations of this bundles;
  5. how to construct the curvature spinors and to investigate its properties;
  6. how to obtain the canonical form of a bilinear form for the 6-dimensional
pseudo-Euclidean space with the even index of the metric;
  7. how to construct the geometric interpretation of isotropic twistors on the
isotropic cone of the 6-dimensional pseudo-Euclidean space with the index equal
to 4;
  8. how to construct the generalization of the Cartan triality principle to
the Klein correspondence;
  9. how to construct the structural constants of the octonion algebra for the
initial induction step?
  In this article, the initial induction step for the induction constructions,
presented in arXiv:1110.4737 and arXiv:1202.0941, is constructed.
