This article is cited in 12 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.

UDC: 514.764.214

MSC: 53C29, 53C50, 53B30

Received: 16.07.2014

DOI: 10.4213/rm9610

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

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