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We prove that given a pseudo-Riemannian conformal structure whose conformalholonomy representation fixes a totally lightlike subspace of arbitrarydimension, there is, wrt. a local metric in the conformal class defined off asingular set, a parallel, totally lightlike distribution on the tangent bundlewhich contains the image of the Ricci-tensor. This generalizes results obtainedfor invariant lightlike lines and planes and closes a gap in the understandingof the geometric meaning of reducibly acting conformal holonomy groups. We showhow this result naturally applies to the classification of geometries admittingtwistor spinors in some low-dimensional split signatures when they aredescribed using conformal spin tractor calculus. Together with already knownresults about generic distributions in dimensions 5 and 6 we obtain a completegeometric description of local geometries admitting real twistor spinors insignatures (3,2) and (3,3). In contrast to the generic case where genericgeometric distributions play an important role, the underlying geometries inthe non-generic case without zeroes turn out to admit integrable distributions.

Reducible conformal holonomy in any metric signature and application to twistor spinors in low dimension