Differential geometry of singular surfaces in R3

• Grant number: 14/22285-0
• Support Opportunities: Scholarships abroad - Research
• Start date: January 12, 2015
• End date: January 28, 2015
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Luciana de Fátima Martins
• Grantee: Luciana de Fátima Martins
• Host Investigator: Juan Jose Nuno Ballesteros
• Host Institution: Instituto de Biociências, Letras e Ciências Exatas (IBILCE). Universidade Estadual Paulista (UNESP). Campus de São José do Rio Preto. São José do Rio Preto , SP, Brazil
• Institution abroad: Universitat de València, Spain
• Associated research grant: 12/24454-8 - Algebraic, geometric and differential topology, AP.TEM

Abstract

The project is to develop research in Geometry/ Yopology using tools of the Singularity Theory and Differential Topology. We aimed to investigate the index of a binary differential equation given by the pair of foliations on a surface M, defined by the principal directions in an isolated singular point of rank 1 M. We also intend to investigate intrinsic and extrinsic invariants of M and its relations with the umbilical curvature at a singular point. (AU)