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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 and 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, p.~53-97. ESI Lectures in Mathematics and Physics. ISBN~978-3-03719-051-7. Available from: https://dx.doi.org/10.4171/051.
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