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 Sfb 288 Differential Geometry and Quantum Physics

Abstract for Sfb Preprint No. 594

Towards a classification of Lorentzian holonomy groups

Th. Leistner

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 $( \mathbb{R} \times SO(n) )\ltimes \mathbb{R}^n$. The main ingredient of such a holonomy group is the $SO(n)$--projection $G:=pr_{SO(n)}(Hol_p(M,h))$ 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.

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Copyright © 1999 Sfb 288, Mathematics 8-5, Strasse des 17 Juni 136, TU-Berlin, 10623 Berlin
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