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

Abstract

We study the problem of prescribing the Ricci curvature in the class of naturally reductive metrics on a compact Lie group. We derive necessary as well as sufficient conditions for the solvability of the equations and provide a series of examples.

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

“…In order to find conditions for solvability, we characterise metrics satisfying (1.2) as critical points of the scalar curvature functional subject to one of three T -dependent constraints. While this characterisation is similar in spirit to the one obtained for compact Lie groups in [APZ20], it bears some conceptual distinctions and requires a different proof. We obtain existence theorems for global maxima and classify some of the other critical points.…”