Holonomy groups of Lorentzian manifolds
Differential Geometry
2016-11-08 v1 General Relativity and Quantum Cosmology
High Energy Physics - Theory
Abstract
In this paper, a survey of the recent results about the classification of the connected holonomy groups of the Lorentzian manifolds is given. A simplification of the construction of the Lorentzian metrics with all possible connected holonomy groups is obtained. As the applications, 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.
Keywords
Cite
@article{arxiv.1611.01551,
title = {Holonomy groups of Lorentzian manifolds},
author = {Anton S. Galaev},
journal= {arXiv preprint arXiv:1611.01551},
year = {2016}
}
Comments
49 pages; this is a survey on Lorentzian holonomy groups and their applications