Conformally flat Lorentzian hypersurfaces in the conformal compactification of Lorentz space

We study conformally flat Lorentzian hypersurfaces in the conformal compactification of Lorentz space R1n+1, which is the projectivized light cone R̂1n+1⊂RPn+2 induced from R2n+3. We establish a Lorentzian version of the local classification theorem of Cartan, in terms of branched channel hypersurfaces for n≥4, and for n=3, in terms of the conformal fundamental forms. For hypersurfaces whose shape operator has complex eigenvalues, we give a necessary condition for being conformally flat in terms of local integrability of distributions.