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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, vol.~93, 5-6, p.~810--815. ISSN~0001-4346. Available from: https://dx.doi.org/10.1134/S0001434613050209.
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