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Geometric deformations of singularities

Grant number: 22/06325-8
Support type:Scholarships in Brazil - Post-Doctorate
Effective date (Start): July 01, 2022
Effective date (End): June 30, 2023
Field of knowledge:Physical Sciences and Mathematics - Mathematics - Geometry and Topology
Principal researcher:Farid Tari
Grantee:Marco Antônio do Couto Fernandes
Home Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil
Associated research grant:19/07316-0 - Singularity theory and its applications to differential geometry, differential equations and computer vision, AP.TEM

Abstract

The research of this project is within singularity theory and its applications to differential geometry and qualitative theory of implicit differential equations. Its aim is to study geometric deformations of singular plane curves and surfaces defined implicitly in the Euclidean and Minkowski spaces, and obtain, in particular, the maximum number of inflection points and vertices (for curves) and umbilic points (for surfaces) that can appear in deformations of such objects. Another aim of the project is to study the generic deformations in the lines of principal curvatures on 1-parameter families of surfaces in Minkowski space. (AU)

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