Invariant prolongation of overdetermined PDE's in projective, conformal and Grassmannian geometry

TL;DR

This paper develops a method to naturally prolong overdetermined invariant differential equations in various parabolic geometries, enhancing the understanding of their structure and solutions.

Contribution

It introduces a systematic procedure for prolonging overdetermined PDEs in projective, conformal, and Grassmannian geometries, expanding on previous work.

Findings

Computed prolongation covariant derivatives for multiple geometries

Provided a unified framework for invariant PDE prolongation

Enhanced understanding of geometric structures in parabolic geometries

Abstract

This is the second in a series of papers on natural modification of the normal tractor connection in a parabolic geometry, which naturally prolongs an underlying overdetermined system of invariant differential equations. We give a short review of the general procedure developed in [5] and then compute the prolongation covariant derivatives for a number of interesting examples in projective, conformal and Grassmannian geometries.