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

C 2008

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

GALAEV, Anton a Thomas LEISTNER

Základní údaje

Originální název

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

Autoři

GALAEV, Anton (643 Rusko, garant, domácí) a Thomas LEISTNER (276 Německo)

Vydání

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

Nakladatel

European Mathematical Society

Další údaje

Jazyk

angličtina

Typ výsledku

Kapitola resp. kapitoly v odborné knize

Obor

10101 Pure mathematics

Stát vydavatele

Rakousko

Utajení

není předmětem státního či obchodního tajemství

Forma vydání

tištěná verze "print"

Odkazy

URL

Kód RIV

RIV/00216224:14310/08:00050991

Organizační jednotka

Přírodovědecká fakulta

ISBN

978-3-03719-051-7

DOI

http://dx.doi.org/10.4171/051

UT WoS

000268749200002

Klíčová slova česky

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

Klíčová slova anglicky

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

Štítky

Pb, rivok

Příznaky

Mezinárodní význam, Recenzováno

Změněno: 15. 6. 2020 14:45, Mgr. Marie Šípková, DiS.

Anotace

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.

Citovat

GALAEV, Anton a Thomas LEISTNER. Holonomy groups of Lorentzian manifolds: classification, examples, and applications. In LEISTNER, Thomas. Recent developments in pseudo-Riemannian geometry. Vienna, Austria: European Mathematical Society, 2008, s. 53-97. ESI Lectures in Mathematics and Physics. ISBN 978-3-03719-051-7. Dostupné z: https://dx.doi.org/10.4171/051.

@inbook{770524,
   author = {Galaev, Anton and Leistner, Thomas and Leistner, Thomas},
   address = {Vienna, Austria},
   booktitle = {Recent developments in pseudo-Riemannian geometry},
   doi = {http://dx.doi.org/10.4171/051},
   keywords = {Holonomy groups; Lorentzian manifolds; parallel spinors; pp-waves},
   howpublished = {tištěná verze "print"},
   language = {eng},
   location = {Vienna, Austria},
   isbn = {978-3-03719-051-7},
   pages = {53-97},
   publisher = {European Mathematical Society},
   title = {Holonomy groups of Lorentzian manifolds: classification, examples, and applications},
   url = {https://www.ems-ph.org/books/book.php?proj_nr=81},
   year = {2008}
}

TY  - CHAP
ID  - 770524
AU  - Galaev, Anton - Leistner, Thomas - Leistner, Thomas
PY  - 2008
TI  - Holonomy groups of Lorentzian manifolds: classification, examples, and applications
VL  - ESI Lectures in Mathematics and Physics
PB  - European Mathematical Society
CY  - Vienna, Austria
SN  - 9783037190517
KW  - Holonomy groups
KW  - Lorentzian manifolds
KW  - parallel spinors
KW  - pp-waves
UR  - https://www.ems-ph.org/books/book.php?proj_nr=81
L2  - https://www.ems-ph.org/books/book.php?proj_nr=81
N2  - 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.
ER  -

GALAEV, Anton a Thomas LEISTNER. Holonomy groups of Lorentzian manifolds: classification, examples, and applications. In LEISTNER, Thomas. \textit{Recent developments in pseudo-Riemannian geometry}. Vienna, Austria: European Mathematical Society, 2008, s.~53-97. ESI Lectures in Mathematics and Physics. ISBN~978-3-03719-051-7. Dostupné z: https://dx.doi.org/10.4171/051.

Podrobný výpis o publikaci