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@article{1111022,
author = {Galaev, Anton},
article_number = {5-6},
doi = {http://dx.doi.org/10.1134/S0001434613050209},
keywords = {holonomy algebra; pseudo-Riemannian manifolds; linear connection; Levi-Civita connection; curvature tensor; Lorentzian manifold},
language = {eng},
issn = {0001-4346},
journal = {Mathematical Notes},
title = {Note on the Holonomy Groups of Pseudo-Riemannian Manifolds},
url = {http://link.springer.com/journal/11006},
volume = {93},
year = {2013}
}
TY - JOUR
ID - 1111022
AU - Galaev, Anton
PY - 2013
TI - Note on the Holonomy Groups of Pseudo-Riemannian Manifolds
JF - Mathematical Notes
VL - 93
IS - 5-6
SP - 810--815
EP - 810--815
SN - 00014346
KW - holonomy algebra
KW - pseudo-Riemannian manifolds
KW - linear connection
KW - Levi-Civita connection
KW - curvature tensor
KW - Lorentzian manifold
UR - http://link.springer.com/journal/11006
N2 - For an arbitrary subalgebra h \subset so(r, s) a polynomial pseudo-Riemannian metric of signature (r + 2, s + 2) is constructed, the holonomy algebra of this metric contains h as a subalgebra. This result shows the essential distinction between the holonomy algebras of pseudoRiemannian manifolds of index greater than or equal to 2 and the holonomy algebras of Riemannian and Lorentzian manifolds.
ER -
GALAEV, Anton. Note on the Holonomy Groups of Pseudo-Riemannian Manifolds. \textit{Mathematical Notes}. 2013, roč.~93, 5-6, s.~810--815. ISSN~0001-4346. Dostupné z: https://dx.doi.org/10.1134/S0001434613050209.
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