Three-dimensional homogeneous generalized Ricci solitons (Q1679444)

A pseudo-Riemannian generalized Ricci soliton is a metric which satisfies the equation \[L_X g + 2 \alpha g\circ X \vee g \circ X - 2 \beta \operatorname{ric} (X,X) = 2 \lambda g\] for some vector field \(X\) and constant \(\alpha, \beta, \lambda\), where \(\operatorname{ric}\) is the Ricci curvature. The author classifies all left-invariant generalized Ricci solitons on 3-dimensional Lie groups \(G\), that is, left-invariant Riemannian or Lorentzian metrics on of \(G\), which satisfy the above equation for some left-invariant vector field \(X\). In this case, the generalized Ricci soliton equation reduces to a system of algebraic equation on the Lie algebra of the group \(G\).