Closed geodesics on Riemannian stacks

• Grant number: 22/11994-6
• Support Opportunities: Scholarships abroad - Research Internship - Doctorate
• Effective date (Start): March 01, 2023
• Effective date (End): May 27, 2023
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Cristián Andrés Ortiz González
• Grantee: Fabricio Valencia Quintero
• Supervisor: Luca Vitagliano
• Host Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil
• Research place: Università degli Studi di Salerno, Italy
• Associated to the scholarship: 20/07704-7 - Morse theory on Lie groupoids and stacks, BP.DR

Abstract

In this project we propose to start the study of the problem concerning the existence of closed geodesics on a Riemannian stack. For that purpose we plan to study the properties of the energy functional defined over stacky curves as well as a proper notion of Jacobi field along stacky geodesics on the Riemannian stack. This proposal is framed in the Fapesp project "Morse theory on Lie groupoids and stacks'' process number 2020/07704-7. (AU)