Certain symmetries of $\mathbb R^2$ with diagonal metrics

Adara M. Blaga

Certain symmetries of $\mathbb R^2$ with diagonal metrics

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arxiv 2410.11969 v3 pith:AB2WKBRI submitted 2024-10-15 math.DG

Adara M. Blaga This is my paper · ORCID

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keywords certaindiagonalmathbbmetricssymmetriesaccordingcoefficientsconcretely

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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
math.DG 2025-01 conditional novelty 4.0 of 10

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.

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