A tour of exceptional geometry
type: Item
instance of: scholarly article
title: A tour of exceptional geometry
zbMATH Open document ID: 1055.53039
published in: Milan Journal of Mathematics
publication date: 2004-09-07T00:00:00Z
review text: \textit{Berger}'s classification of holonomy groups [Bull. Soc. Math. Fr. 83, 279--330 (1955; Zbl 0068.36002)], includes \(SU(3)\) and the exceptional holonomy groups \( G_{2}\), Spin(7). After a discussion of \(G_{2}\) and its manifestation and the definition of various groups the author shows that in certain simple situations it is possible to calculate the Levi-Civita connection \(\nabla\) directly from knowledge of the exterior derivative \(d\) and to calculate it for specific metrics on \(7\)-manifolds. Before the last section the author studies the \(G_{2}\), Spin(7), \(SU(3)\) structures respectively and in the last section he gives some topological observations that are relevant for the construction of orbifolds.
reviewed by: M. Belkhelfa
Mathematics Subject Classification ID: 53C29
Mathematics Subject Classification ID: 53C25
Mathematics Subject Classification ID: 53C55
zbMATH DE Number: 2099243
zbMATH Keywords: special holonomy
zbMATH Keywords: differential forms
zbMATH Keywords: Hermitian manifold
author: Simon Salamon
MaRDI profile type: Publication
full work available at URL: s00032-003-0015-0
OpenAlex ID: W2051620161
Wikidata QID: Q124986919
DOI: 10.1007/S00032-003-0015-0
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description: scientific article; zbMATH DE number 2099243