About the differential geometry of certain frontals in Euclidean 3-space

Author(s)

Samuel Paulino dos Santos

• Document type: Doctoral Thesis
• Press: São José do Rio Preto. 2022-10-11.
• Institution: Universidade Estadual Paulista (Unesp). Instituto de Biociências Letras e Ciências Exatas. São José do Rio Preto
• Defense date: 2022-08-31
• Advisor: Luciana de Fátima Martins; Kentaro Saji

Abstract

This work seeks to study the geometry of some especific classes of singular surfaces which are not necessarily fronts or non-degenerated singularities. We study the singular surfaces D4 , when it is given as a bifurcation set of a deformation; this surface is a front which has a degenerated singular point. We also study a class of singular surfaces called σ-edges, which are frontals, but are fronts or non-degenerated singular points in very specific cases. At last, we study the geometry of the focal set of singular surface which are frontal but not front in every singular point; such surfaces are called pure frontals. (AU)

• FAPESP's process: 18/17712-7 - Geometry of singular surfaces
• Grantee: Samuel Paulino dos Santos
• Support Opportunities: Scholarships in Brazil - Doctorate