The classification of 3-dimensional Lorentzian affine hypersurfaces with parallel cubic form

We study Lorentzian affine hypersurfaces in Rn+1Rn+1 with parallel cubic form with respect to the Levi-Civita connection of the affine metric. As main result, a complete classification of such non-degenerate affine hypersurfaces in R4R4 is given.