Singularity theory and the geometry of submanifolds of the Minkowski space

• Grant number: 11/21240-4
• Support Opportunities: Regular Research Grants
• Start date: March 01, 2012
• End date: February 28, 2014
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Farid Tari
• Grantee: Farid Tari
• Host Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil

Abstract

The project is on problems in singularity theory and on its applications to differential geometry. One part of the project deals with the study of singularities of curves and surfaces which takes into consideration the flat geometry of these objects. The second part deals with the geometry of submanifolds in the Minkowski spaces. We deal mainly with the case where the induced metric changes signature on the submanifolds. (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)

DIAS, FABIO SCALCO; TARI, FARID. ON THE GEOMETRY OF THE CROSS-CAP IN MINKOWSKI 3-SPACE AND BINARY DIFFERENTIAL EQUATIONS. TOHOKU MATHEMATICAL JOURNAL, v. 68, n. 2, p. 293-328, JUN 2016. (11/21240-4, 11/01946-0, 14/00304-2)

IZUMIYA, SHYUICHI; TARI, FARID. Apparent contours in Minkowski 3-space and first order ordinary differential equations. Nonlinearity, v. 26, n. 4, p. 911-932, APR 2013. (11/21240-4)

SINHA, RAUL OSET; TARI, FARID. Projections of surfaces in R-4 to R-3 and the geometry of their singular images. REVISTA MATEMATICA IBEROAMERICANA, v. 31, n. 1, p. 33-50, 2015. (11/21240-4, 10/01501-5)