Please join us for lunch after the talk.
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).