Geometry on deformations of S1 singularities

TL;DR

This paper investigates one-parameter deformations of S1 singularities, focusing on their differential geometric properties, and introduces a form representation using diffeomorphisms and isometries to analyze these properties.

Contribution

It presents a new form representation of deformations of S1 singularities using diffeomorphisms and isometries, facilitating geometric analysis.

Findings

Characterization of deformations using diffeomorphisms and isometries

Analysis of Whitney umbrellas in the deformation process

Insights into the geometric properties of S1 singularities

Abstract

To study a one parameter deformation of an $S_1$ singularity taking into consideration its differential geometric properties, we give a form representing the deformation using only diffeomorphisms on the source and isometries of the target. Using this form, we study differential geometric properties of $S_1$ singularities and the Whitney umbrellas appearing in the deformation.