3 papers
math.DG2025
Stable umbilical points of a W-congruence
Marcos Craizer, Ronaldo Alves Garcia
The class of -congruences is a central object of Projective Differential Geometry. Nevertheless, their singularities has not been extensively studied. In this paper we prove a c…
math.DG2025
A discrete analog of Segre's theorem on spherical curves
Samuel Pacitti Gentil, Marcos Craizer
We prove a discrete analog of a certain four-vertex theorem for space curves. The smooth case goes back to the work of Beniamino Segre and states that a closed and smooth curve who…
math.DG2024
Envelopes of Bisection Lines of Polygons
Joel Albertacci Marques da Silva, Marcos Craizer
A bisection line divides a convex planar curve into two parts with equal areas. It is natural to study the envelope of these lines, which in general present singularities. The poly…