Spinor formalism and the geometry of six-dimensional Riemannian spaces
  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. 
K. V. Andreev
math-ph math.DG math.MP math.QA