Towards a classification of Lorentzian holonomy groups

Abstract

If the holonomy representation of an $(n+2)$--dimensional simply-connected Lorentzian manifold $(M,h)$ admits a degenerate invariant subspace its holonomy group is contained in the parabolic group $(\mathbb{R}\times SO(n))⋉{\mathbb{R}}^n$. The main ingredient of such a holonomy group is the SO(n)--projection $G:=p{r}_{SO(n)}(Ho{l}_p(M,h))$ and one may ask whether it has to be a Riemannian holonomy group. In this paper we show that this is the case if $G\subset U(n/2)$ or if the irreducible acting components of $G$ are simple.

73 pages, 3 figures

References in corpus (1)

• The spaces of curvature tensors for holonomy algebras of Lorentzian manifolds

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