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

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

2003-09-17

arxiv.org/abs/math/0309274v1

Mathematics

Differential Geometry

13 pages

Scientific paper

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 the first part math.DG/0305139. We draw consequences for the existence of parallel spinors on Lorentzian manifolds.

Affiliated with

Also associated with

No associations

Rating

Towards a classification of Lorentzian holonomy groups. Part II: Semisimple, non-simple weak-Berger algebras does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Towards a classification of Lorentzian holonomy groups. Part II: Semisimple, non-simple weak-Berger algebras, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Towards a classification of Lorentzian holonomy groups. Part II: Semisimple, non-simple weak-Berger algebras will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-137720