Conformal geometry of homogeneous manifolds

• Grant number: 24/19272-5
• Support Opportunities: Regular Research Grants
• Start date: July 01, 2025
• End date: June 30, 2027
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Mobility Program: SPRINT - Projetos de pesquisa - Mobilidade
• Principal Investigator: Viviana Jorgelina Del Barco
• Grantee: Viviana Jorgelina Del Barco
• Principal researcher abroad: Andrei Moroianu
• Institution abroad: Centre National de la Recherche Scientifique, France
• Host Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil
• Associated research grant: 23/15089-9 - Aspects of the conformal and Riemannian geometry of Lie groups and their compact quotients., AP.R

Abstract

The present project focuses on the study of Killing tensors and locally conformally product (LCP) structures on homogeneous manifolds. It explores these mathematical objects' implications in theoretical physics and Riemannian geometry. The main objectives are to investigate Killing tensors in solvable Lie groups and symmetric spaces, and to further understand the structure of LCP manifolds through advanced Lie theoretical techniques. The project builds on a pre-existing collaboration of the PRs, aiming to expand the understanding of these geometrical structures with postdoctoral and student involvement. (AU)