14 citations · 20 across the 30 of their papers we have counts for
36 papers
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…
Singularities of Discrete Indefinite Affine Minimal Surfaces
Marcos Craizer
A smooth affine minimal surface with indefinite metric can be obtained from a pair of smooth non-intersecting spatial curves by Lelieuvre's formulas. These surfaces may present sin…
Moutard hyperquadrics and generalized Darboux directions
Fernanda Py Silva Cordeiro, Marcos Craizer
The higher order contact of a quadric with a surface in -space at a non-degenerate point is obtained by the Moutard quadric in the Darboux direction. In this paper, we discuss t…
Discrete Asymptotic Nets with Constant Affine Mean Curvature
Anderson Reis de Vargas, Marcos Craizer
In this paper we define the class of constant affine mean curvature (CAMC) discrete asymptotic nets, which contains the well-known classes of affine spheres and affine minimal asym…
Singularities of Discrete Improper Indefinite Affine Spheres
Anderson Reis de Vargas, Marcos Craizer
We consider in this paper discrete improper affine spheres based on asymptotic nets. In this context, we distinguish the discrete edges and vertices that must be considered singula…
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…