Search

In this paper, we give the generic classification of the singularities of 3-parameter line congruences in $\mathbb {R}^{4}$. We also classify the generic singularities of normal and Blaschke (affine) normal congruences.

We construct a Legendrian version of envelope theory. A tangential family is a one-parameter family of rays emanating tangentially from a regular plane curve. The Legendrian graph of the family is the union of the Legendrian lifts of the family curves in the projectivized cotangent bundle $PT^*\mathbb{R}^2$. We study the singularities of Legendrian graphs and their stability under small tangential deformations. We also find normal forms of their projections into the plane. This allows us to interpret the beak-to-beak perestroika as the apparent contour of a deformation of the double Whitney umbrella singularity $A_1^\pm$.

Search Results

Refine search

Refine search

Actions for selected content:

2 results

Singularities of 3-parameter line congruences in $\mathbb {R}^{4}$

LEGENDRIAN GRAPHS GENERATED BY TANGENTIAL FAMILY GERMS

Search Results

Refine search

Refine search

Actions for selected content:

Save Search

2 results

Singularities of 3-parameter line congruences in $\mathbb {R}^{4}$

LEGENDRIAN GRAPHS GENERATED BY TANGENTIAL FAMILY GERMS