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

Abstract: The prescribed Ricci curvature problem consists in finding 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 left-invariant 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).

Mathematics

Audience: researchers in the topic

Geometry Seminar - University of Florence

Series comments: If you are interested in attending, please send a message to daniele.angella@unifi.it or francesco.pediconi@unifi.it.