Non-Holonomic Connections Following \'Elie Cartan

TL;DR

This paper revisits Cartan's 1928 work on strongly non-holonomic distributions, establishing a foundation for applying Cartan's method of equivalence to broader classes of non-holonomic geometrical structures.

Contribution

It extends Cartan's original framework to more general non-holonomic distributions using his method of equivalence.

Findings

Develops a systematic approach for analyzing strongly non-holonomic distributions.

Prepares groundwork for future invariants in non-holonomic geometry.

Bridges classical Cartan theory with modern geometric analysis.

Abstract

In this note we revisit E. Cartan's address at the 1928 International Congress of Mathematicians at Bologna, Italy. The distributions considered here will be of the same class as those considered by Cartan, a special type which we call strongly non-holonomic. We set up the groundwork for using Cartan's method of equivalence (a powerful tool for obtaining invariants associated to geometrical objects), to more general non-holonomic distributions.