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For every codimension two spacelike submanifold of a Lorentz manifold andeach choice of a normal lightlike vector field, we introduce a canonical way toconstruct a tractor conformal bundle. We characterize when the inducedconnection of a such submanifold defines a tractor connection and then, in thiscase, when this tractor conformal bundle with the induced connection isstandard for the induced metric. Finally, the normality condition for thistractor conformal bundle endowed with the induced connection is characterizedin terms of a strong relationship between the intrinsic and the extrinsicgeometry of the starting spacelike submanifold.

Normal tractor conformal bundles and codimension two spacelike submanifolds in Lorentzian manifolds