Twistor Hermitian form
= Twistor Hermitian form
{title2=$h(Z,W)=\omega^A\overline{\rho}_A+\pi_{A'}\overline{\eta}^{A'}$}
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>.