Note on the Holonomy Groups of Pseudo-Riemannian Manifolds

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Authors

GALAEV Anton

Year of publication 2013
Type Article in Periodical
Magazine / Source Mathematical Notes
MU Faculty or unit

Faculty of Science

Citation
Web http://link.springer.com/journal/11006
Doi http://dx.doi.org/10.1134/S0001434613050209
Field General mathematics
Keywords holonomy algebra; pseudo-Riemannian manifolds; linear connection; Levi-Civita connection; curvature tensor; Lorentzian manifold
Description 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.
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