Introducing the Classical Method of Moving Frames

TL;DR

This paper explains how the classical method of moving frames, developed by Cartan, helps identify differential invariants of geometric objects under various transformation groups.

Contribution

It provides an expository overview of applying the moving frames method to determine invariants under Euclidean, affine, and conformal groups.

Findings

Method effectively identifies differential invariants of curves and surfaces.

Applicable to Euclidean, affine, and conformal transformations.

Clarifies historical and mathematical significance of Cartan's approach.

Abstract

The method of moving frames (rep\`ere mobile) was used by Elie Cartan as a way of organizing the identification of differential invariants and solving equivalence problems. In this expository paper, we discuss how moving frames are used to determine differential invariants of curves and surfaces under the action of Euclidean, affine and conformal transformation groups.