Towards a classification of Lorentzian holonomy groups
نویسنده
چکیده
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 (R×SO(n))⋉R. The main ingredient of such a holonomy group is the SO(n)–projection G := prSO(n)(Holp(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 ⊂ U(n/2) or if the irreducible acting components of G are simple.
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