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 Sfb 288 Differential Geometry and Quantum Physics

Abstract for Sfb Preprint No. 595

Towards a classification of Lorentzian holonomy groups. Part II: Semisimple, non-simple weak-Berger algebras.

Th. Leistner

The holonomy group of an $(n+2)$--dimensional simply-connected, indecomposable but non-irreducible Lorentzian manifold $(M,h)$ 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 always the case, completing our results of \cite{leistner03}. We draw consequences for the existence of parallel spinors on Lorentzian manifolds.

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