The prescribed Ricci curvature problem on three‐dimensional unimodular Lie groups

Timothy Buttsworth

Mathematische Nachrichten, 2019, vol. 292, issue 4, 747-759

Abstract: Let G be a three‐dimensional unimodular Lie group, and let T be a left‐invariant symmetric (0,2)‐tensor field on G. We provide the necessary and sufficient conditions on T for the existence of a pair (g,c) consisting of a left‐invariant Riemannian metric g and a positive constant c such that Ric(g)=cT, where Ric(g) is the Ricci curvature of g. We also discuss the uniqueness of such pairs and show that, in most cases, there exists at most one positive constant c such that Ric(g)=cT is solvable for some left‐invariant Riemannian metric g.

Date: 2019
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