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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
References:
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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
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  • https://doi.org/10.1070/RM2015v070n02ABEH004947
  • https://www.mathnet.ru/eng/rm/v70/i2/p55
    • This publication is cited in the following 11 articles:
    1. José M. M. Senovilla, “Semi-Riemannian manifolds with linear differential conditions on the curvature”, Anal.Math.Phys., 14:3 (2024)  crossref
    2. H. Mahdiloo, P. Ahmadi, M. Hassani, “Actions with cohomogeneity zero or one on the de Sitter space dSn-1,1”, Differential Geometry and its Applications, 97 (2024), 102180  crossref
    3. Hanci Chi, Ioannis Chrysikos, Eivind Schneider, “Decomposable (5, 6)-solutions in eleven-dimensional supergravity”, Journal of Mathematical Physics, 64:6 (2023)  crossref
    4. Alawadhi R., Berman D.S., White Ch.D., Wikeley S., “The Single Copy of the Gravitational Holonomy”, J. High Energy Phys., 2021, no. 10, 229  crossref  mathscinet  isi
    5. Dikarev A., “On Holonomy of Weyl Connections in Lorentzian Signature”, Differ. Geom. Appl., 76 (2021), 101759  crossref  mathscinet  isi
    6. Dikarev A., Galaev A.S., “Parallel Spinors on Lorentzian Weyl Spaces”, Mon.heft. Math., 196:1 (2021), 39–58  crossref  mathscinet  isi
    7. Ch. Volkhausen, “Local type III metrics with holonomy in G2”, Ann. Glob. Anal. Geom., 56:1 (2019), 113–136  crossref  mathscinet  isi
    8. A. Fino, I. Kath, “Holonomy groups of g(2)()-manifolds”, Trans. Am. Math. Soc., 371:11 (2019), 7725–7755  crossref  mathscinet  isi
    9. A. S. Galaev, “Holonomy classification of Lorentz-Kahler manifolds”, J. Geom. Anal., 29:2 (2019), 1075–1108  crossref  mathscinet  isi  scopus
    10. Helga Baum, Thomas Leistner, Tutorials, Schools, and Workshops in the Mathematical Sciences, Geometric Flows and the Geometry of Space-time, 2018, 1  crossref
    11. M. Gutiérrez, O. Müller, “Compact Lorentzian holonomy”, Differential Geom. Appl., 48 (2016), 11–22  crossref  mathscinet  zmath  isi  elib  scopus
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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    Abstract page:908
    Russian version PDF:345
    English version PDF:54
    References:100
    First page:58
     
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