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The interplay between Lie groupoids and Riemannian Geometry

Grant number: 19/14777-3
Support type:Scholarships in Brazil - Post-Doctorate
Effective date (Start): April 01, 2020
Effective date (End): March 31, 2022
Field of knowledge:Physical Sciences and Mathematics - Mathematics - Geometry and Topology
Principal researcher:Ivan Struchiner
Grantee:Mateus Moreira de Melo
Home 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)

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