Geometry of singular surfaces in $\mathbb{R}^4$

• Grant number: 19/00194-6
• Support Opportunities: Scholarships in Brazil - Post-Doctoral
• Start date: August 01, 2019
• End date: August 22, 2019
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: João Nivaldo Tomazella
• Grantee: Pedro Benedini Riul
• Host Institution: Centro de Ciências Exatas e de Tecnologia (CCET). Universidade Federal de São Carlos (UFSCAR). São Carlos , SP, Brazil
• Associated research grant: 14/00304-2 - Singularities of differentiable mappings: theory and applications, AP.TEM

Abstract

In this project we propose to investigate corank $1$ singular surfaces in $\mathbb{R}^4$ from several points of view: associating it with the geometry of space curves, singular $3$-manifolds in $\mathbb{R}^5$ and projections into singular surfaces in $\mathbb{R}^3$. Moreover, we aim to extend the study to corank $1$ surfaces in $\mathbb{R}^n$, $n>4$.

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)

RIUL, PEDRO BENEDINI; SOARES RUAS, MARIA APARECIDA; SACRAMENTO, ANDREA DE JESUS. Singular 3-manifolds in R-5. REVISTA DE LA REAL ACADEMIA DE CIENCIAS EXACTAS FISICAS Y NATURALES SERIE A-MATEMATICAS, v. 116, n. 1, JAN 2022. (19/00194-6, 19/21181-0)

RIUL, P. BENEDINI; SINHA, R. OSET. RELATING SECOND ORDER GEOMETRY OF MANIFOLDS THROUGH PROJECTIONS AND NORMAL SECTIONS. PUBLICACIONS MATEMATIQUES, v. 65, n. 1, p. 389-407, 2021. (19/00194-6)