Generic singularities of affine distance functions and plane congruences

TL;DR

This paper classifies the typical singularities in affine distance functions and plane congruences in four-dimensional space, providing a comprehensive understanding of their generic behaviors.

Contribution

It introduces a classification of generic singularities for affine normal plane congruences and affine distance functions in four-dimensional space.

Findings

Classification of generic singularities for affine normal plane congruences

Identification of singularities in affine distance functions

Extension of singularity theory to affine geometric contexts

Abstract

In this paper, we classify the generic singularities of 2-parameter plane congruences in $\mathbb{R^4}$ and the generic singularities of affine normal plane congruences. We also study the generic singularities of the family of affine distance functions.