Singularities of affine equidistants: projections and contacts

TL;DR

This paper classifies stable singularities of affine quidistants for certain submanifolds in  space, using projection and contact singularity methods, within specific dimension constraints.

Contribution

It provides a classification of stable singularities of affine quidistants for n-dimensional submanifolds in  space under certain dimension conditions, advancing singularity theory.

Findings

Classification of stable singularities for affine quidistants.

Application of projection and contact methods to singularity analysis.

Results valid for pairs of dimensions where q n.

Abstract

Using standard methods for studying singularities of projections and of contacts, we classify the stable singularities of affine $\lambda$-equidistants of $n$-dimensional closed submanifolds of $\mathbb R^q$, for $q\leq 2n$, whenever $(2n,q)$ is a pair of nice dimensions.