Normal tractor conformal bundles and codimension two spacelike submanifolds in Lorentzian manifolds (Q2672332)

Given a space-like submanifold \(M\) of codimension two in a Lorentzian manifold, and given any normal light-like vector field on \(M\), the authors construct in a canonical way a tractor conformal bundle (which is a particular vector bundle) on \(M\). They characterize the case when the induced connection of \(M\) defines a tractor connection and when, in this case, the constructed tractor conformal bundle endowed with the induced connection is standard for the induced metric of \(M\). They also give the normality condition for this tractor conformal bundle endowed with the induced connection in terms of a relationship between the intrinsic and the extrinsic geometries of \(M\).