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Note on the holonomy groups of pseudo-Riemannian manifolds

Anton S. Galaev
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Abstract

For an arbitrary subalgebra $\mathfrak{h}\subset\mathfrak{so}(r,s)$, a polynomial pseudo-Riemannian metric of signature $(r+2,s+2)$ is constructed, the holonomy algebra of this metric contains $\mathfrak{h}$ as a subalgebra. This result shows the essential distinction of the holonomy algebras of pseudo-Riemannian manifolds of index bigger or equal to 2 from the holonomy algebras of Riemannian and Lorentzian manifolds.

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Anton S. Galaev. 2004-06-21. Note on the holonomy groups of pseudo-Riemannian manifolds. https://doi.org/10.1134/s0001434613050209

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