Note on the Holonomy Groups of Pseudo-Riemannian Manifolds
| Authors | |
|---|---|
| Year of publication | 2013 |
| Type | Article in Periodical |
| Magazine / Source | Mathematical Notes |
| MU Faculty or unit | |
| 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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