Criteria for D_4 singularities of wave fronts

TL;DR

This paper provides simple criteria to identify D_4 singularities in wave fronts and explores how singular curvatures behave near these points, enhancing understanding of wave front singularities.

Contribution

It introduces straightforward criteria for D_4 singularities and analyzes curvature behaviors near these singularities in wave fronts.

Findings

Criteria for D_4 singularities established

Behavior of singular curvatures near D_4^+ singularities analyzed

Enhanced understanding of wave front singularities

Abstract

We give useful and simple criteria for determining D_4 singularities of wave fronts. As an application, we investigate behaviors of singular curvatures of cuspidal edges near D_4^+ singularities.