Projective null twistor space ($PN=\{[Z]\in {\mathbb{CP}}^3:h(Z,Z)=0\}$)

The five-real-dimensional space of projective null twistors. A projective line lies entirely in it precisely when its corresponding two-plane is totally isotropic for the twistor Hermitian form. Such lines represent real points of Minkowski conformal compactification. Two independent null twistors lie on one such line exactly when $h(X,Y)=0$.