The interplay between Lie groupoids and Riemannian Geometry

• Grant number: 19/14777-3
• Support Opportunities: Scholarships in Brazil - Post-Doctoral
• Effective date (Start): April 01, 2020
• Effective date (End): April 17, 2023
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Ivan Struchiner
• Grantee: Mateus Moreira de Melo
• Host Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil
• Associated research grant: 16/23746-6 - Algebraic, topological and analytical techniques in differential geometry and geometric analysis, AP.TEM

Abstract

This project lies at the interface of differential geometry and Lie theory, particularly in the connections of the Riemannian and Poisson geometry with Lie groupoids. More precisely, the project is focused on using Lie groupoids as models for singular spaces and developing Riemannian geometry in this context by studying compatible metrics on Lie groupoids, namely Riemannian groupoids. These singular spaces are called Riemannian stacks. We intend to use the stacks tools to prove the existence of closed geodesics for compact Riemannian stacks. We plan to investigate how "far'' a Riemannian groupoid is to be a proper Lie groupoid. This might lead to understanding new obstructions for a Lie groupoid be a Riemannian groupoid. (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)

ALEXANDRINO, MARCOS M.; INAGAKI, MARCELO K.; DE MELO, MATEUS; STRUCHINER, IVAN. ie groupoids and semi-local models of singular Riemannian foliation. ANNALS OF GLOBAL ANALYSIS AND GEOMETRY, v. 61, n. 3, p. 593-619, APR 2022. (15/22059-2, 19/14777-3, 16/23746-6)

DEL HOYO, MATIAS; DE MELO, MATEUS. On invariant linearization of Lie groupoids. LETTERS IN MATHEMATICAL PHYSICS, v. 111, n. 4, AUG 2021. (19/14777-3)