Spinor formalism for \(n=6\)
type: Item
instance of: scholarly article
title: Spinor formalism for \(n=6\)
zbMATH Open document ID: 1014.53028
author: K. V. Andreev
published in: Russian Mathematics
publication date: 2002-06-09T00:00:00Z
review text: 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.
reviewed by: Mircea Craioveanu
Mathematics Subject Classification ID: 53C27
Mathematics Subject Classification ID: 15A66
zbMATH DE Number: 1752611
zbMATH Keywords: complex Euclidean space
zbMATH Keywords: Clifford equation
zbMATH Keywords: spinor formalism
zbMATH Keywords: Norden operator
zbMATH Keywords: complex-analytic Riemann space
zbMATH Keywords: complex-analytic vector bundle
zbMATH Keywords: connection
zbMATH Keywords: curvature tensor
zbMATH Keywords: Cartan triplicity principle for two quadrics
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1752611