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

Seminar schedule

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).