Note on the holonomy groups of pseudo-Riemannian manifolds

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.

6 pages, final version

References in corpus (2)

• The spaces of curvature tensors for holonomy algebras of Lorentzian manifolds
• Isometry groups of Lobachevskian spaces, similarity transformation groups of Euclidean spaces and Lorentzian holonomy groups

Cited by in corpus (1)

• Holonomy algebras of Einstein pseudo-Riemannian manifolds