Geodesics on surfaces with singular metrics

• Grant number: 12/03960-2
• Support Opportunities: Research Grants - Visiting Researcher Grant - International
• Start date: September 01, 2012
• End date: September 27, 2012
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Farid Tari
• Grantee: Farid Tari
• Visiting researcher: Alexey Remizov
• Visiting researcher institution: École Polytechnique, France
• Host Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil

Abstract

For generic surface M with a generic singular metric, the locus of degeneracy of the metric is a smooth curve on M called the parabolic curve. At each point on the parabolic curve there is a unique isotropic direction (or lightlike direction). Alexey Remizov established the generic behaviour of the geodesic on M at parabolic points where the unique isotropic direction is transverse to the parabolic curve. The aim of this project is to complete the study of the generic behaviour of the geodesic on M and consider the case where the unique isotropic direction is tangent to the parabolic curve. (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)

CHERTOVSKIH, R. A.; REMIZOV, A. O.. On Pleated Singular Points of First-Order Implicit Differential Equations. JOURNAL OF DYNAMICAL AND CONTROL SYSTEMS, v. 20, n. 2, p. 197-206, APR 2014. (12/03960-2)

REMIZOV, A. O.. On the local and global properties of geodesics in pseudo-Riemannian metrics. DIFFERENTIAL GEOMETRY AND ITS APPLICATIONS, v. 39, p. 36-58, APR 2015. (12/03960-2)