Recognition Problem of Frontal Singularities

TL;DR

This paper surveys the recognition problem of frontal singularities, providing explicit normal forms, combining previous results, and applying these to classify singularities in tangent surfaces of null curves in Lorentz three-manifolds.

Contribution

It offers a comprehensive survey with explicit normal forms for recognizing frontal singularities and applies these to classify singularities in tangent surfaces of null curves.

Findings

Explicit normal forms for frontal singularities

Classification of singularities in tangent surfaces of null curves

Recognition results for singularities in Lorentz three-manifolds

Abstract

This is a survey article on recognition problem of frontal singularities. We specify geometrically several frontal singularities and then we solve the recognition problem of such singularities, giving explicit normal forms. We combine the recognition results by K. Saji and several arguments on openings, which was performed for the classification of singularities of tangent surfaces (tangent developables) by the author. As an application of our solutions of recognition problem of frontal singularities, we announce the classification of singularities appearing in tangent surfaces of generic null curves which are ruled by null geodesics in general Lorentz three-manifolds, mentioning related recognition results and open problems.