Parallel spinors and holonomy groups on pseudo-Riemannian spin manifolds
type: Item
instance of: scholarly article
title: Parallel spinors and holonomy groups on pseudo-Riemannian spin manifolds
zbMATH Open document ID: 0928.53027
DOI: 10.1023/A:1006556630988
author: Helga Baum
author: Ines Kath
published in: Annals of Global Analysis and Geometry
publication date: 2000-01-02T00:00:00Z
full work available at URL: https://arxiv.org/abs/math/9803080
review text: The authors describe the possible holonomy groups \(H\) of simply connected irreducible non locally-symmetric pseudo-Riemannian spin manifolds which admit parallel spinors and calculate the dimension \(N\) of the space of parallel spinors. More precisely, they prove that if \(N > 1\), then the holonomy \(H\) belongs to one of the series: \[ (SU(p,q),\;N=2) \qquad (Sp(p,q),\;N= p+q+1) \] or is the exceptional group \(G_2^{\mathbb C} \subset SO(7,7)\), \(N=2\). If \(N=1\), then \(H\) is one of the following linear groups: \( G_2 \subset SO(7)\), \(G^*_{2 (2)} \subset SO(4,3)\), \(\text{Spin}(7) \subset SO(8)\), \(\text{Spin}(4,3) \subset SO(4,4)\), \(\text{Spin}(7)^{\mathbb C}\subset SO(8,8).\)
Mathematics Subject Classification ID: 53C27
Mathematics Subject Classification ID: 53C29
Mathematics Subject Classification ID: 53C50
zbMATH DE Number: 1271808
zbMATH Keywords: holonomy groups
zbMATH Keywords: parallel spinors
zbMATH Keywords: pseudo-Riemannian manifolds
reviewed by: Dmitri Alekseevsky
MaRDI profile type: Publication
arXiv ID: math/9803080
description: scientific article