Singularities of 3-parameter line congruences in $\mathbb{R}^4$

TL;DR

This paper classifies the typical singularities of 3-parameter line congruences and affine normal congruences in four-dimensional space, providing a comprehensive understanding of their geometric behavior.

Contribution

It offers the first generic classification of singularities for these congruences in , including affine normal cases, advancing the geometric theory.

Findings

Classification of generic singularities of 3-parameter line congruences in 

Classification of singularities of Blaschke (affine) normal congruences

Provides a framework for understanding geometric singularities in higher dimensions

Abstract

In this paper, we give the generic classification of the singularities of 3-parameter line congruences in $\mathbb{R}^4$. We also classify the generic singularities of Blaschke (affine) normal congruences.