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@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.
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