Understanding singularities in Cartan's and NSF geometric structures

TL;DR

This paper explores the connection between Cartan's geometric approach to third order ODEs and the Null Surface Formulation, extending both frameworks to include caustics and singularities that naturally occur in these models.

Contribution

It establishes a relationship between Cartan's approach and NSF, and generalizes both to incorporate caustics and singularities.

Findings

Unified geometric framework for third order ODEs and NSF

Extension of models to include caustics and singularities

Enhanced understanding of singularities in geometric structures

Abstract

In this work we establish a relationship between Cartan's geometric approach to third order ODEs and the 3-dim Null Surface Formulation (NSF). We then generalize both constructions to allow for caustics and singularities that necessarily arise in these formalisms.