if we take the standard pseudo-euclidean quadratic form on the imaginary split octonions and then restrict it to the linear subspace carved out by "x*k=0" for k a given non-zero point on the light cone, then is the restriction of the quadratic form to the subspace the square of a linear form? and can this explain how the projective light cone for the restriction could be a projective plane? ??or something like that??