in the case of lorentzian four-metrics, the self-dual connection and curvature are the complex conjugates of the anti-self-dual connection and curvature and take (complex conjugate) values in the lie algebras sl( 2, c ) r and sl( 2, c ) l. the two-component spinor approach to the cartan equations for 4-metrics can be summarized, using notation which is compatible with the above, as follows. the line element, given by eqs. (42) and (43), can be written: there is a good chance this thread will be dumped
how about let's change the thread to speaking in morse code .. / -.. --- -. .----. - / .-.. .. -.- . / - .... .. ... / --. .- -- .