Connections with torsion, parallel spinors and geometry of Spin(7) manifolds
type: Item
instance of: scholarly article
title: Connections with torsion, parallel spinors and geometry of Spin(7) manifolds
zbMATH Open document ID: 1073.53065
author: Stefan Ivanov
published in: Mathematical Research Letters
publication date: 2004-12-29T00:00:00Z
full work available at URL: https://arxiv.org/abs/math/0111216
review text: The existence of a parallel spinor imposes restrictions on the holonomy group. In the case of Levi-Civita connections the possible Riemannian holonomy groups are \(\text{SU}(n)\), \(\text{Sp}(n)\), \(G_2\) and \(\text{Spin}(7)\). In this paper, the author studies the existence of parallel spinors with respect to a metric connection with skew-symmetric torsion in manifolds of dimension \(8\). He proves that such a manifold must be a \(\text{Spin}(7)\)-manifold. He shows also the vanishing of the \(A\)-genus and obtains a linear relation between Betti numbers of a compact \(\text{Spin}(7)\)-manifold which is locally (but not globally) conformally equivalent to a space with closed fundamental 4-form. Moreover, a general solution to the Killing spinor equations is also presented.
Mathematics Subject Classification ID: 53C27
Mathematics Subject Classification ID: 53C29
Mathematics Subject Classification ID: 53C25
Mathematics Subject Classification ID: 53C55
Mathematics Subject Classification ID: 81T30
zbMATH DE Number: 2123920
zbMATH Keywords: structure
zbMATH Keywords: torsion
zbMATH Keywords: Dirac operator
zbMATH Keywords: parallel spinors
zbMATH Keywords: Killing spinor equations
reviewed by: Marisa Fernández
MaRDI profile type: Publication
arXiv ID: math/0111216
DOI: 10.4310/MRL.2004.V11.N2.A3
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description: scientific article