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

TL;DR

This paper studies the prescribed Ricci curvature problem for naturally reductive metrics on non-compact simple Lie groups, providing conditions for solvability and exploring specific examples.

Contribution

It introduces new conditions for solving the prescribed Ricci curvature equations in this geometric setting and analyzes several illustrative cases.

Findings

Derived solvability conditions for the Ricci curvature equations

Identified specific examples satisfying the conditions

Enhanced understanding of naturally reductive metrics on non-compact groups

Abstract

We investigate the prescribed Ricci curvature problem in the class of left-invariant naturally reductive Riemannian metrics on a non-compact simple Lie group. We obtain a number of conditions for the solvability of the underlying equations and discuss several examples.