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Aspects of the conformal and Riemannian geometry of Lie groups and their compact quotients.

Grant number: 23/15089-9
Support Opportunities:Regular Research Grants
Duration: February 01, 2024 - January 31, 2026
Field of knowledge:Physical Sciences and Mathematics - Mathematics - Geometry and Topology
Principal Investigator:Viviana Jorgelina Del Barco
Grantee:Viviana Jorgelina Del Barco
Host Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil
Associated researchers: Andrei Moroianu

Abstract

The present research proposal is aimed at the study of special geometric structures on Lie groups and their compact quotients, when they exist. The general objective of the project is to determine algebraic and topological constraints for a Lie group to carry certaub Riemannian or conformal structures.Different types of geometric structures will be considered on such manifolds, namely, conformal Killing tensors and $\rG_2$-structures on Riemannian Lie groups, and locally conformally product and Weyl-Einstein structures, mostly related to conformal classes of metrics that are invariant under left-translations on a Lie group. In differential geometry, and especially after Milnor's work in 1976, Lie groups endowed with left-invariant metrics, constitute a source of examples and counterexamples to the most varied problems in geometry. This in part is due to the fact that these are manifolds with a manageable geometry, since they allow the use of Lie theoretical techniques. The relevance of Lie groups in differential geometry motivates the present research proposal. (AU)

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