Bifurcations of robust features on surfaces in the Minkowski 3-space

TL;DR

This paper investigates how certain special curves on surfaces in Minkowski 3-space change under small deformations, focusing on features like degenerate metrics, principal curvature lines, parabolic curves, and zero mean curvature loci.

Contribution

It provides a detailed bifurcation analysis of key geometric features on surfaces in Minkowski 3-space, which was not previously comprehensively studied.

Findings

Bifurcation behavior of degenerate metric loci

Analysis of discriminant lines of principal curvature

Characterization of parabolic and zero mean curvature curves

Abstract

We obtain the bifurcation of some special curves on generic 1-parameter families of surfaces in the Minkowski 3-space. The curves treated here are the locus of points where the induced pseudo metric is degenerate, the discriminant of the lines principal curvature, the parabolic curve and the locus of points where the mean curvature vanishes.