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arXiv · 1607.03233

The Prescribed Ricci Curvature Problem on Three-Dimensional Unimodular Lie Groups

Timothy Buttsworth
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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 almost all cases, there exists at most one positive constant c such that Ric(g) = cT is solvable for some left-invariant Riemannian metric g.

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Timothy Buttsworth. 2016-07-12. The Prescribed Ricci Curvature Problem on Three-Dimensional Unimodular Lie Groups. https://arxiv.org/abs/1607.03233

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