Graph immersions with parallel cubic form

We consider non-degenerate graph immersions into affine space An+1 whose cubic form is parallel with respect to the Levi-Civita connection of metric. There exists a correspondence between such and pairs (J,?), where J an n-dimensional real Jordan algebra ? trace on J. Every immersion can be extended complete symmetric covering maximal connected component zero in set quasi-regular elements It improper hypersphere if only corresponding nilpotent. In this case it complete, Euclidean immersion, polynomial as globally defining function. classify all hyperspheres up dimension 5. As special we describe Cayley hypersurfaces quotient algebras. Our algebraic approach used study also other classes form.