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Uspekhi Mat. Nauk, 2015, Volume 70, Issue 2(422), Pages 55–108 (Mi umn9610)  

This article is cited in 4 scientific papers (total in 4 papers)

Holonomy groups of Lorentzian manifolds

A. S. Galaev

University of Hradec Králové, Hradec Králové, Czech Republic

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.

DOI: https://doi.org/10.4213/rm9610

Full text: PDF file (938 kB)
References: PDF file   HTML file

English version:
Russian Mathematical Surveys, 2015, 70:2, 249–298

Bibliographic databases:

UDC: 514.764.214
MSC: 53C29, 53C50, 53B30
Received: 16.07.2014

Citation: A. S. Galaev, “Holonomy groups of Lorentzian manifolds”, Uspekhi Mat. Nauk, 70:2(422) (2015), 55–108; 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
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\yr 2015
\vol 70
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\pages 55--108
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\transl
\jour Russian Math. Surveys
\yr 2015
\vol 70
\issue 2
\pages 249--298
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. M. Gutiérrez, O. Müller, “Compact Lorentzian holonomy”, Differential Geom. Appl., 48 (2016), 11–22  crossref  mathscinet  zmath  isi  elib  scopus
    2. Volkhausen Ch., “Local Type III Metrics With Holonomy in G2”, Ann. Glob. Anal. Geom., 56:1 (2019), 113–136  crossref  isi
    3. Fino A., Kath I., “Holonomy Groups of G(2)()-Manifolds”, Trans. Am. Math. Soc., 371:11 (2019), 7725–7755  crossref  isi
    4. Galaev A.S., “Holonomy Classification of Lorentz-Kahler Manifolds”, J. Geom. Anal., 29:2 (2019), 1075–1108  crossref  isi
  • Успехи математических наук Russian Mathematical Surveys
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