Invariant prolongation of overdetermined PDEs in projective, conformal, and Grassmannian geometry

Abstract

This is the second in a series of articles on a natural modification of the normal tractor connection on parabolic geometries, which naturally prolongs an underlying overdetermined system of invariant differential equations. We give a short review of the general procedure developed in Hammerl et al. (preprint) and then compute the prolongation covariant derivatives for a number of interesting examples in projective, conformal, and Grassmannian geometries.