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

Romina Arroyo (Queensland)

Abstract

One of the most important challenges of Riemannian geometry is to understand the Ricci curvature tensor. An open problem related with it is to find 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 discuss this problem within the class of naturally reductive metrics when \(M\) is a compact simple Lie group.

This talk is based on work in progress with Artem Pulemotov (The University of Queensland).