Geodesic
Holonomy groups of Lorentzian manifolds
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 70 (2015) no. 2, pp. 249-298

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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. 
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     author = {A. S. Galaev},
     title = {Holonomy groups of {Lorentzian} manifolds},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
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     url = {http://geodesic.mathdoc.fr/item/RM_2015_70_2_a1/}
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A. S. Galaev. Holonomy groups of Lorentzian manifolds. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 70 (2015) no. 2, pp. 249-298. http://geodesic.mathdoc.fr/item/RM_2015_70_2_a1/