M. A. C. Fernandes

collaborators

4 papers

math.DG2025

Some results on evolutoids of convex curves in $2$ -dimensional space forms

Ady Cambraia Junior, Alessandro Gaio Chimenton, Marco AntÃ´nio do Couto Fernandes +1

Let $M_{c}$ be a $2$ -dimensional space form of constant curvature $c = - 1, 0, 1$ and $I^^{3}$ a smooth, closed, convex curve in $M_{c}$ . We explicitly parametrize the \textit{ $I^\pm$ -evolutoid} o…

math.DG2025

On vertices and inflections of singular plane curves

James William Bruce, Marco AntÃ´nio do Couto Fernandes, Farid Tari

Given the germ of a smooth plane curve $({f (x, y) = 0}, 0) \subset (K^{2}, 0), K = R, C$ , with an isolated singularity, we define two invariants $I_{f}$ a…

math.DG2025

Geometric deformations of implicit curves

Marco AntÃ´nio do Couto Fernandes, Samuel Paulino dos Santos

Let f = 0 be an implicit singular plane curve. When deforming f = 0, inflections and vertex emerge from the singularities. In this papper, we classify the deformations of f = 0 wit…

math.DG2024

On geometric invariants of singular plane curves

J. W. Bruce, M. A. C. Fernandes, F. Tari

Given a germ of a smooth plane curve $({f (x, y) = 0}, 0) \subset (K^{2}, 0), K = R, C$ , with an isolated singularity, we define two invariants $I_{f}$ and $V_…

Some results on evolutoids of convex curves in 2-dimensional space forms

On vertices and inflections of singular plane curves

Geometric deformations of implicit curves

On geometric invariants of singular plane curves

Some results on evolutoids of convex curves in $2$ -dimensional space forms