Advanced search
Start date
Betweenand

Curves in Minkowski space

Grant number: 10/20301-7
Support type:Scholarships in Brazil - Doctorate
Effective date (Start): May 01, 2011
Effective date (End): February 28, 2015
Field of knowledge:Physical Sciences and Mathematics - Mathematics - Geometry and Topology
Principal researcher:Ana Claudia Nabarro
Grantee:Andrea de Jesus Sacramento
Home Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil
Associated research grant:08/54222-6 - Singularities, geometry and differential equations, AP.TEM

Abstract

The problems for the thesis are part of a larger project that study the geometry of submanifolds in Minkowski space by using singularity theory. For her thesis, Andrea will study the geometry of curves in 3-Minkowski space. It may happen that the normal vector and binormal vector of the curve are lightlike, as can also happen that the normal plane or osculating plane is lightlike at some points on the curve. These points have not the Serret-Frenet formulas for curves. Also the curvature and/or torsion of the curve at these points are not defined. However, the contacts of the curve with planes and pseudo-spheres are well defined. Andrea will study families of height functions and distance squared functions over the curve to obtain geometric informations about the curve, including informations about the dual and focal set of the curves. We will also work with curves in timelike surfaces in Minkowski space and study the focal set of these curves and also obtain geometric results. We hope to find some invariants using the theory of contact. If there's enough time, the student will study properties of closed curves in 3-Minkowski space and will investigate the geometry of surfaces generated by curves. (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)
IZUMIYA, SHYUICHI; NABARRO, ANA CLAUDIA; SACRAMENTO, ANDREA DE JESUS. HOROSPHERICAL AND HYPERBOLIC DUAL SURFACES OF SPACELIKE CURVES IN DE SITTER SPACE. JOURNAL OF SINGULARITIES, v. 16, p. 180-193, DEC 2017. Web of Science Citations: 0.
NABARRO, ANA CLAUDIA; SACRAMENTO, ANDREA DE JESUS. Focal set of curves in the Minkowski space near lightlike points. PUBLICATIONES MATHEMATICAE-DEBRECEN, v. 88, n. 3-4, p. 487-510, 2016. Web of Science Citations: 0.
IZUMIYA, SHYUICHI; NABARRO, ANA CLAUDIA; SACRAMENTO, ANDREA DE JESUS. Pseudo-spherical normal Darboux images of curves on a timelike surface in three dimensional Lorentz-Minkowski space. JOURNAL OF GEOMETRY AND PHYSICS, v. 97, p. 105-118, NOV 2015. Web of Science Citations: 2.
Academic Publications
(References retrieved automatically from State of São Paulo Research Institutions)
SACRAMENTO, Andrea de Jesus. Curves in the Minkowski space. 2015. Doctoral Thesis - Universidade de São Paulo (USP). Instituto de Ciências Matemáticas e de Computação São Carlos.

Please report errors in scientific publications list by writing to: cdi@fapesp.br.