On affine geometry and singularities

• Grant number: 11/21126-7
• Support Opportunities: Scholarships abroad - Research Internship - Doctorate
• Start date: September 01, 2012
• End date: August 31, 2013
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Marcelo José Saia
• Grantee: Luis Florial Espinoza Sánchez
• Supervisor: Juan Jose Nuño Ballesteros
• Host Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil
• Institution abroad: Universitat de València, Spain
• Associated to the scholarship: 10/08631-1 - Affine geometry and singularities, BP.DR

Abstract

We study the geometry of immersed surfaces in the 4-affine space, we will characterize these from singularities which appear in the contact of the surfaces with hyperplanes obtained from the height function, since these are affine invariants. Mochida, Romero-Fuster and Ruas described this problem in the Euclidean case and obtained results of the geometry of a surface. We intend to develop the affine case that has not yet been explored in the general case of codimension 2. (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)

NUNO-BALLESTEROS, JUAN J.; SANCHEZ, LUIS. Affine metrics of locally strictly convex surfaces in affine 4-space. Geometriae Dedicata, v. 183, n. 1, p. 1-24, AUG 2016. (11/21126-7)