Singularities of Gauss maps of wave fronts with non-degenerate singular points

TL;DR

This paper investigates the singularities of Gauss maps of wave fronts with non-degenerate singular points, linking geometric properties and curvature behavior to classify singularities and analyze their relations.

Contribution

It provides new characterizations of Gauss map singularities based on geometric properties and curvature behavior near cuspidal edges.

Findings

Characterization of Gauss map singularities via geometric properties.

Relation between Gaussian curvature boundedness and singularity types.

Analysis of extended height functions on fronts with non-degenerate singular points.

Abstract

We study singularities of Gauss maps of fronts and give characterizations of types of singularities of Gauss maps by geometric properties of fronts which are related to behavior of bounded principal curvatures. Moreover, we investigate relation between a kind of boundedness of Gaussian curvatures near cuspidal edges and types of singularities of Gauss maps of cuspidal edges. Further, we consider extended height functions on fronts with non-degenerate singular points.