Canonical frames for Gl(2)-structures

TL;DR

This paper develops a canonical frame for Gl(2)-structures, addressing their equivalence problem, and applies the results to contact equivalence of ODEs and specific vector distributions.

Contribution

It introduces a canonical frame construction for Gl(2)-structures, solving the equivalence problem and characterizing structures defined by ODEs.

Findings

Canonical frame for Gl(2)-structures constructed

Solution to the equivalence problem provided

Characterization of structures defined by ODEs included

Abstract

We construct a canonical frame for an arbitrary Gl(2)-structure thus solving the equivalence problem for Gl(2)-structures. Our treatment includes also a problem of contact equivalence of ordinary differential equations and applies to certain classes of vector distributions. Additionally we characterise Gl(2)-structures which are defined by ODEs.