GLOBAL ASPECTS IN FINSLER AND LORENTZIAN GEOMETRY

• Grant number: 10/11934-6
• Support Opportunities: Scholarships in Brazil - Post-Doctoral
• Effective date (Start): December 01, 2010
• Effective date (End): November 30, 2012
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Paolo Piccione
• Grantee: Ricardo Gallego Torrome
• Host Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil
• Associated research grant: 07/03192-7 - Submanifold geometry and Morse theory in finite and infinite dimensions, AP.TEM

Abstract

We propose to investigate some global aspects of Finsler and Lorentziangeometry and the interplay between them. The problems are structured in twodifferent types. The first type is concerned with different aspects of (semi)-Randers spaces and the links with stationary space-times in the framework ofLorentzian geometry. The second type of problems concern Finsler geometry.In particular we would like to investigate a generalization of the Gauss-Bonnetformula for general Finsler structures and provide a suitable theory for theRicci flow in Finsler geometry.

Scientific publications

(5)

(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)

TORROME, RICARDO GALLEGO. Fiber averaged dynamics associated with the Lorentz force equation. JOURNAL OF GEOMETRY AND PHYSICS, v. 86, p. 43-65, DEC 2014. (10/11934-6)

TORROME, RICARDO GALLEGO; PICCIONE, PAOLO; VITORIO, HENRIQUE. On Fermat's principle for causal curves in time oriented Finsler spacetimes. Journal of Mathematical Physics, v. 53, n. 12, DEC 2012. (10/11934-6)

TORROME, RICARDO GALLEGO. A second-order differential equation for a point charged particle. INTERNATIONAL JOURNAL OF GEOMETRIC METHODS IN MODERN PHYSICS, v. 14, n. 4, APR 2017. (10/11934-6)

TORROME, RICARDO GALLEGO. ON THE CONVEX INVARIANCE IN FINSLER GEOMETRY. SYMMETRY-CULTURE AND SCIENCE, v. 23, n. 2, p. 8-pg., 2012-01-01. (10/11934-6)

TORROME, RICARDO GALLEGO; GRATUS, JONATHAN. k-Jet field approximations to geodesic deviation equations. INTERNATIONAL JOURNAL OF GEOMETRIC METHODS IN MODERN PHYSICS, v. 15, n. 12, DEC 2018. (10/11934-6)