Local twistor

In differential geometry, the local twistor bundle is a specific vector bundle with connection that can be associated to any conformal manifold, at least locally. Intuitively, a local twistor is an association of a twistor space to each point of space-time, together with a conformally invariant connection that relates the twistor spaces at different points. This connection can have holonomy that obstructs the existence of "global" twistors (that is, solutions of the twistor equation in open sets).