How to find the holonomy algebra of a Lorentzian manifold
type: Item
instance of: scholarly article
title: How to find the holonomy algebra of a Lorentzian manifold
zbMATH Open document ID: 1320.53055
published in: Letters in Mathematical Physics
publication date: 2015-02-16T00:00:00Z
full work available at URL: https://arxiv.org/abs/1110.1998
review text: As it is well known, manifolds with exceptional holonomy play an important role in string theory, supergravity and \(M\)-theory. In the paper under review, the author explains how one can find the holonomy algebra of an arbitrary Riemannian or Lorentzian manifold. Using the de Rham and Wu decompositions, this problem is reduced to the case of locally indecomposable manifolds (see also the previous paper by the author [Classical Quantum Gravity 31, No. 13, Article ID 135007, 13 p. (2014; Zbl 1301.53043)]).
Mathematics Subject Classification ID: 53C29
Mathematics Subject Classification ID: 53C25
Mathematics Subject Classification ID: 53C50
Mathematics Subject Classification ID: 81T30
zbMATH DE Number: 6403874
zbMATH Keywords: Lorentzian manifold
zbMATH Keywords: holonomy group
zbMATH Keywords: holonomy algebra
zbMATH Keywords: de Rham-Wu decomposition
author: Anton Galaev
reviewed by: Radu Iordănescu
describes a project that uses: DifferentialGeometry
MaRDI profile type: Publication
OpenAlex ID: W3102929501
arXiv ID: 1110.1998
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cites work: Codazzi spinors and globally hyperbolic manifolds with special holonomy
cites work: On the full holonomy group of Lorentzian manifolds
cites work: Globally Hyperbolic Lorentzian Manifolds with Special Holonomy Groups
cites work: Q3142327
cites work: Q4720334
cites work: On the holonomy of Lorentzian metrics
cites work: Supersymmetry, holonomy and Kundt spacetimes
cites work: Pseudo-Riemannian metrics with parallel spinor fields and vanishing Ricci tensor
cites work: Holonomy groups and spacetimes
cites work: Very Special Relativity
cites work: Metrics with vanishing quantum corrections
cites work: The spin holonomy group in general relativity
cites work: The spaces of curvature tensors for holonomy algebras of Lorentzian manifolds
cites work: METRICS THAT REALIZE ALL LORENTZIAN HOLONOMY ALGEBRAS
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cites work: One component of the curvature tensor of a Lorentzian manifold
cites work: On the local structure of Lorentzian Einstein manifolds with parallel distribution of null lines
cites work: On the de Rham-Wu decomposition for Riemannian and Lorentzian manifolds
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cites work: Some Applications of the Infinitesimal-Holonomy Group to the Petrov Classification of Einstein Spaces
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cites work: M-theory on Spin(7) manifolds
cites work: Breaking the sanserifM-waves
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cites work: Holonomy groups of compact Riemannian manifolds: A classification in dimensions up to ten
cites work: Methods of holonomy theory for Ricci-flat Riemannian manifolds
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DOI: 10.1007/S11005-014-0741-Y
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description: scientific article