Spinor formalism for \(n=6\) (Q1599395)

The author describes the \(6\)-dimensional spinor formalism by means of the Norden operators \(\eta_{\;aa_1}^{\alpha}\) and \(\eta_{\alpha}^{\;aa_1},\;\alpha=1,\dots ,6\), \(a,a_1=1,\dots ,4\), that give isomorphisms between the complex Euclidean space \(\mathbb{CR}_6\) and the bivector space of \(\mathbb{C}^4\) [see \textit{A. P. Norden}, Izv. Vyssh. Zaved., Mat. No.~1(8), 156--164 (1959; Zbl 0085.15603)]. Applications of this formalism to the local study of connections on certain complex-analytic vector bundles over a \(6\)-dimensional complex-analytic Riemann space and to the proof of the Cartan triplicity principle for two quadrics in the \(7\)-dimensional complex projective space are given.