Geometric invariants of cuspidal edges

TL;DR

This paper introduces a normal form for cuspidal edges that simplifies their geometric analysis and studies invariants that classify these edges up to third order, clarifying their interrelations.

Contribution

It provides a new normal form for cuspidal edges using source diffeomorphisms and target isometries, and analyzes their differential geometric invariants.

Findings

Normal form for cuspidal edges established

Invariants determine cuspidal edges up to third order

Relations between invariants clarified

Abstract

We give a normal form of the cuspidal edge which uses only diffeomorphisms on the source and isometries on the target. Using this normal form, we study differential geometric invariants of cuspidal edges which determine them up to order three. We also clarify relations between these invariants.