On the geometry of surfaces in R4

• Grant number: 12/00066-9
• Support type: Scholarships in Brazil - Doctorate
• Effective date (Start): April 01, 2012
• Effective date (End): January 31, 2016
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal researcher: Farid Tari
• Grantee: Jorge Luiz Deolindo Silva
• Home Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil

Abstract

The project is on the geometry of surfaces in R4 from the point of view of singularity theory. The aim of the project is to investigate the local and multi-local geometric properties of such surfaces using the theory of contact and of implicit differential equations. For some surfaces, the project includes global problems such as finding and estimate of the number of components of a special curve on the surface (which captures some aspects of the extrinsic geometry of the surface) and an estimate of the number of special points on such curve. (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)

DEOLINDO SILVA, JORGE LUTZ; KABATA, YUTARO. Projective classification of jets of surfaces in 4-space. HIROSHIMA MATHEMATICAL JOURNAL, v. 49, n. 1, p. 35-46, MAR 2019. (12/00066-9)

DEOLINDO-SILVA, JORGE LUIZ. Cross-Ratio Invariants for Surfaces in 4-Space. BULLETIN OF THE BRAZILIAN MATHEMATICAL SOCIETY, v. 52, n. 3, p. 591-612, SEP 2021. (12/00066-9)

Academic Publications

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

SILVA, Jorge Luiz Deolindo. Cr-invariants for surfaces in R^4. 2016. Doctoral Thesis - Universidade de São Paulo (USP). Instituto de Ciências Matemáticas e de Computação (ICMC/SB) São Carlos.