Geometry of singular surfaces

• Grant number: 18/17712-7
• Support Opportunities: Scholarships in Brazil - Doctorate
• Start date: December 01, 2018
• End date: August 03, 2022
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Luciana de Fátima Martins
• Grantee: Samuel Paulino dos Santos
• Host Institution: Instituto de Biociências, Letras e Ciências Exatas (IBILCE). Universidade Estadual Paulista (UNESP). Campus de São José do Rio Preto. São José do Rio Preto , SP, Brazil
• Associated research grant: 14/00304-2 - Singularities of differentiable mappings: theory and applications, AP.TEM
• Associated scholarship(s): 19/10156-4 - Geometry of singular surfaces, BE.EP.DR

Abstract

The PhD project is about the Geometry of singular surfaces in R3, using Singularity Theory tools. This project intends to investigate local properties of singular surfaces, such as those of rotation obtained from singular generative curves, as well as those that are focal surfaces of singular surfaces of rotation, hoping to obtain geometric properties, invariants and relations between geometrical properties of the focal surface and of the initial surface of rotation. It is also intended to explore other singular surfaces, such as generalized helicoids, among others that may arise during the study. The project also contemplates theinvariants associated with singularities andof formulas related to them. Through a scholarship application for research abroad (BEPE), we intend to maintain a partnership with K. Saji and K. Teramoto, from the University of Kobe, Japan, who are authors of the main scientific articles that are reference for this project. (AU)

Scientific publications

(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)

MARTINS LUCIANA F.; KENTARO SAJI; SAMUEL P. DOS SANTOS; KEISUKE TERAMOTO. Singular surfaces of revolution with prescribed unbounded mean curvature. Anais da Academia Brasileira de Ciências, v. 91, n. 3, 2019-09-02. (16/21226-5, 18/17712-7, 18/19610-7)

SAJI, KENTARO; DOS SANTOS, SAMUEL PAULINO. Geometry of bifurcation sets of generic unfoldings of corank two functions. MONATSHEFTE FUR MATHEMATIK, v. 196, n. 3, JUL 2021. (18/17712-7, 19/10156-4)

Academic Publications

(References retrieved automatically from State of São Paulo Research Institutions)

SANTOS, Samuel Paulino dos. About the differential geometry of certain frontals in Euclidean 3-space. 2022. Doctoral Thesis - Universidade Estadual Paulista (Unesp). Instituto de Biociências Letras e Ciências Exatas. São José do Rio Preto São José do Rio Preto.