Holonomy groups of Lorentzian manifolds

被引：9
作者：
Galaev, A. S. [1 ]
机构：
[1] Univ Hradec Kralove, Hradec Kralove, Czech Republic
来源：
RUSSIAN MATHEMATICAL SURVEYS | 2015年 / 70卷 / 02期
关键词：
Lorentzian manifold; holonomy group; holonomy algebra; Walker manifold; Einstein equation; recurrent spinor field; conformally flat manifold; 2-symmetric Lorentzian manifold; PSEUDO-RIEMANNIAN MANIFOLDS; CONFORMALLY-FLAT; KAHLERIAN MANIFOLDS; CURVATURE TENSORS; PARALLEL SPINORS; METRICS; CLASSIFICATION; ALGEBRAS; SPACES; SUBMANIFOLDS;
D O I：
10.1070/RM2015v070n02ABEH004947
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
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.
引用
收藏
页码：249 / 298
页数：50
相关论文
共 142 条
  • [41] Holonomy groups of pseudo-quaternionic-Kahlerian manifolds of non-zero scalar curvature
    Bezvitnaya, Natalia I.
    [J]. ANNALS OF GLOBAL ANALYSIS AND GEOMETRY, 2011, 39 (01) : 99 - 105
  • [42] Structure of second-order symmetric Lorentzian manifolds
    Blanco, Oihane F.
    Sanchez, Miguel
    Senovilla, Jose M. M.
    [J]. JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY, 2013, 15 (02) : 595 - 634
  • [43] Complete classification of second-order symmetric spacetimes
    Blanco, Oihane F.
    Sanchez, Miguel
    Senovilla, Jose M. M.
    [J]. SPANISH RELATIVITY MEETING (ERE 2009), 2010, 229
  • [44] Bolsinov A, 2014, J DIFFER GEOM, V97, P377
  • [45] BOREL A, 1952, CR HEBD ACAD SCI, V234, P1835
  • [46] BOUBEL C, 2003, PREPUBLICATION LENS, V315
  • [47] Boubel Ch., 2007, ANN FAC SCI TOULOUSE, V16, P427, DOI 10.5802/afst.1156
  • [48] Boyer CP, 2010, IRMA LECT MATH THEOR, V16, P39, DOI 10.4171/079-1/3
  • [49] Holonomy, decomposability, and relativity1
    Brannlund, J.
    Coley, A.
    Hervik, S.
    [J]. CANADIAN JOURNAL OF PHYSICS, 2009, 87 (03) : 241 - 243
  • [50] Supersymmetry, holonomy and Kundt spacetimes
    Brannlund, J.
    Coley, A.
    Hervik, S.
    [J]. CLASSICAL AND QUANTUM GRAVITY, 2008, 25 (19)
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