Twistor Formulation of Some Partial Differential Equations

Twistor theory has been invented by R. Penrose in order to generalize gravity. He introduced a geometrical model for Minkowski space. This geometrical setup has been generalized in solving particle differential equations. In particular zero-rest-mass field equation have been treated this way as a Contour integral of complex twistor function. In our study we consider geometrical interpretations and solutions of conformal field equations. We also studied Twistors in curved space-time and related this study to the problem of quantum gravity.