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

页码：249 / 298

页数：50

共 142 条

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