# On pairs of geometric foliations on a cuspidal edge

## TL;DR

This paper investigates the topological arrangements of principal curvature lines, asymptotic, and characteristic curves on cuspidal edges, showing they are determined by the surface's 3-jet parametrization.

## Contribution

It provides a detailed analysis of how the local geometry of cuspidal edges influences the configuration of key curvature-related curves.

## Key findings

- Configurations depend on the 3-jet of the parametrization.
- Topological types are classified based on jet data.
- Results apply both in the parametrization domain and on the surface.

## Abstract

We study the topological configurations of the lines of principal curvature, the asymptotic and characteristic curves on a cuspidal edge, in the domain of a parametrization of this surface as well as on the surface itself. Such configurations are determined by the 3-jets of a parametrization of the surface.