 Twistor Hermitian form

For $Z=(\omega ,\pi )$ and $W=(\eta ,\rho )$ the displayed Hermitian form has signature $(2,2)$. It is zero on every pair of vectors in $W_x=\{(ix\pi ,\pi )\}$ when $x$ is Hermitian, that is, Lorentzian real. Conversely a transverse totally isotropic two-plane is such a graph with $x$ Hermitian. This gives the Lorentzian reality structure on twistor space.