C 2008

Holonomy groups of Lorentzian manifolds: classification, examples, and applications

GALAEV, Anton and Thomas LEISTNER

Basic information

Original name

Holonomy groups of Lorentzian manifolds: classification, examples, and applications

Authors

GALAEV, Anton (643 Russian Federation, guarantor, belonging to the institution) and Thomas LEISTNER (276 Germany)

Edition

Vienna, Austria, Recent developments in pseudo-Riemannian geometry, p. 53-97, 45 pp. ESI Lectures in Mathematics and Physics, 2008

Publisher

European Mathematical Society

Other information

Language

English

Type of outcome

Kapitola resp. kapitoly v odborné knize

Field of Study

10101 Pure mathematics

Country of publisher

Austria

Confidentiality degree

není předmětem státního či obchodního tajemství

Publication form

printed version "print"

References:

RIV identification code

RIV/00216224:14310/08:00050991

Organization unit

Faculty of Science

ISBN

978-3-03719-051-7

DOI

UT WoS

000268749200002

Keywords (in Czech)

Holonomy groups, Lorentzian manifolds, parallel spinors, pp-waves

Keywords in English

Holonomy groups; Lorentzian manifolds; parallel spinors; pp-waves

Tags

Tags

International impact, Reviewed
Změněno: 15/6/2020 14:45, Mgr. Marie Šípková, DiS.

Abstract

V originále

We review recent developments in the theory of Lorentzian holonomy groups focussing on the classification results. We present the list of indecomposable, nonirreducible Lorentzian holonomy groups, explain the idea of its proof, and describe a method of constructing metrics which realise all the possible groups. This method is then used to construct many examples of metrics. Finally, we give some applications for the existence of parallel spinors and a short outlook on other signatures. As a new result we obtain the holonomy classification for indecomposable, non-irreducible Lorentzian Einstein spaces.