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Russian Mathematical Surveys, 2015, Volume 70, Issue 2, Pages 249–298
DOI: https://doi.org/10.1070/RM2015v070n02ABEH004947 (Mi rm9610) 		 
This article is cited in 11 scientific papers (total in 11 papers)

Holonomy groups of Lorentzian manifolds

A. S. Galaev

University of Hradec Králové, Hradec Králové, Czech Republic
English version PDF (875 kB) Citations (11) Russian version article
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DOI: https://doi.org/10.1070/RM2015v070n02ABEH004947
Abstract: This paper contains a survey of recent results on classification of the connected holonomy groups of Lorentzian manifolds. A simplification of the construction of Lorentzian metrics with all possible connected holonomy groups is obtained. The Einstein equation, Lorentzian manifolds with parallel and recurrent spinor fields, conformally flat Walker metrics, and the classification of 2-symmetric Lorentzian manifolds are considered as applications.
Bibliography: 123 titles.
Keywords: Lorentzian manifold, holonomy group, holonomy algebra, Walker manifold, Einstein equation, recurrent spinor field, conformally flat manifold, 2-symmetric Lorentzian manifold.
Received: 16.07.2014
Bibliographic databases:
Document Type: Article
UDC: 514.764.214
MSC: 53C29, 53C50, 53B30
Language: English
Original paper language: Russian
Citation: A. S. Galaev, “Holonomy groups of Lorentzian manifolds”, Russian Math. Surveys, 70:2 (2015), 249–298
Citation in format AMSBIB
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\by A.~S.~Galaev
\paper Holonomy groups of Lorentzian manifolds
\jour Russian Math. Surveys
\yr 2015
\vol 70
\issue 2
\pages 249--298
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    • This publication is cited in the following 11 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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