Closed geodesics on Riemannian stacks

• Grant number: 22/11994-6
• Support Opportunities: Scholarships abroad - Research Internship - Doctorate
• Start date: March 01, 2023
• End date: 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
• Institution abroad: 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)

Scientific publications

(The scientific publications listed on this page originate from the Web of Science or SciELO databases. Their authors have cited FAPESP grant or fellowship project numbers awarded to Principal Investigators or Fellowship Recipients, whether or not they are among the authors. This information is collected automatically and retrieved directly from those bibliometric databases.)

VALENCIA, FABRICIO. Novikov type inequalities for orbifolds. MATHEMATISCHE ANNALEN, v. N/A, p. 30-pg., 2025-06-02. (20/07704-7, 24/14883-6, 22/11994-6)

ORTIZ, CRISTIAN; VALENCIA, FABRICIO. Morse theory on Lie groupoids. MATHEMATISCHE ZEITSCHRIFT, v. 307, n. 3, p. 55-pg., 2024-07-01. (22/11994-6, 20/07704-7, 22/09234-3)