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

[31] G2-holonomy metrics connected with a 3-Sasakian manifold
Bazaikin, Ya. V.
Malkovich, E. G.
[J]. SIBERIAN MATHEMATICAL JOURNAL, 2008, 49 (01) : 1 - 4
[32] On the new examples of complete noncompact Spin(7)-holonomy metrics
Bazaikin, Ya. V.
[J]. SIBERIAN MATHEMATICAL JOURNAL, 2007, 48 (01) : 8 - 25
[33] Globally hyperbolic Lorentzian spaces with special holonomy groups
Bazaikin, Ya. V.
[J]. SIBERIAN MATHEMATICAL JOURNAL, 2009, 50 (04) : 567 - 579
[34] BAZAYKIN YAV, 2009, SIB MAT ZH, V4, P721
[35] BAZAYKIN YAV, 2007, SIB MAT ZH, V1, P11
[36] BERARDBERGERY I, 1997, B SOC MATH FRANCE, V125, P93
[37] BERARDBERGERY I, 1993, P S PURE MATH, V54, P27
[38] Berger M., 1955, Bulletin de la Societe Mathematique de France, V83, P279, DOI DOI 10.24033/BSMF.1464
[39] Besse A.L., 1987, ERGEB MATH GRENZGEB, V10
[40] Holonomy algebras of pseudo-hyper-Kahlerian manifolds of index 4
Bezvitnaya, Natalia I.
[J]. DIFFERENTIAL GEOMETRY AND ITS APPLICATIONS, 2013, 31 (02) : 284 - 299

← 1 2 3 4 5 6 7 8 9 10 →