The prescribed Ricci curvature problem for naturally reductive metrics on simple Lie groups

Início: 23/07/2020 17:00

Término: 23/07/2020 18:00

Palestrante: Romina Arroyo (Universidad Nacional Cordoba)

E-mail do Palestrante:

Resumo: One of the most important challenges of Riemannian geometry is to understand the Ricci curvature tensor. An interesting open problem related with it is to find a Riemannian metric whose Ricci curvature is prescribed, that is, a Riemannian metric $g$ and a real number $c>0$ satisfying [ operatorname{Ric} (g) = c T, ] for some fixed symmetric $(0, 2)$-tensor field $T$ on a manifold $M,$ where $operatorname{Ric} (g)$ denotes the Ricci curvature of $g.$ The aim of this talk is to discuss this problem within the class of naturally reductive metrics when $M$ is a simple Lie group, and present recently obtained results in this setting. This talk is based on joint works with Mark Gould (The University of Queensland) Artem Pulemotov (The University of Queensland) and Wolfgang Ziller (University of Pennsylvania).