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.
Certain symmetries of $\mathbb R^2$ with diagonal metrics
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abstract
We put into light the Killing vector fields on $\mathbb R^2$ endowed with a family of diagonal Riemannian metrics. According to certain restrictions on the Lam\'{e} coefficients, we concretely describe the symmetries of the metric.
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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.