4 papers
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…
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…
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…
Boundedness of geometric invariants near a singularity which is a suspension of a singular curve
Luciana F. Martins, Kentaro Saji, Samuel P. dos Santos +1
Near a singular point of a surface or a curve, geometric invariants diverge in general, and the orders of diverge, in particular the boundedness about these invariants represent ge…