For diagonal metrics on R^2, the paper derives and solves the equations ∇V = Q, giving explicit Ricci vector fields and classifying them under certain separability assumptions.
On the potential vector fields of soliton-type equatio ns, Axioms 13(7), 476 (2024)
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Constructing Ricci vector fields on $\mathbb R^2$ with a diagonal metric
For diagonal metrics on R^2, the paper derives and solves the equations ∇V = Q, giving explicit Ricci vector fields and classifying them under certain separability assumptions.