1204.0194 (K. V. Andreev)

Spinor formalism and the geometry of six-dimensional Riemannian spaces    [PDF]

K. V. Andreev

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.

View original: http://arxiv.org/abs/1204.0194