3 papers
math.DG2026
Geometry on principal curvature surfaces
Luciana F. Martins, Kentaro Saji, Samuel P. dos Santos +1
We study the geometry of the principal curvature surface associated with a Whitney umbrella. This surface is obtained by extending the Whitney umbrella in the normal direction by i…
math.DG2025
Helicoidal surfaces of frontals in Euclidian space as deformations of surfaces of revolution, with singularities
Luciana F. Martins, Samuel P. dos Santos
We investigate helicoidal surfaces in three-dimensional Euclidean space whose profile curves are frontals. Using the framework of Legendre curves and framed surfaces, we establish…
math.DG2025
Geometric deformations of implicit curves
Marco Antônio 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…