Conformal and projective tractors from 2-frame bundlesby the dressing field method

Abstract

This paper is devoted to the study of conformal and projective structures, and especially their connections, in the language of 2-frames, or [Formula: see text]-structures of second order. While their normal Cartan connections are well-known, we use the dressing field method to obtain their local, mostly gauge invariant, connections. Lastly, we recall how to obtain the tractor bundle from conformal structures, and then show that we can define a projective tractor bundle using the same kind of construction.