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

@article{Buttsworth2016ThePR,
  title={The prescribed Ricci curvature problem on three‐dimensional unimodular Lie groups},
  author={Timothy Buttsworth},
  journal={Mathematische Nachrichten},
  year={2016},
  volume={292},
  pages={747 - 759}
}
  • T. Buttsworth
  • Published 12 July 2016
  • Mathematics
  • Mathematische Nachrichten
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… 

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