In mathematics, specifically in differential geometry, isothermal coordinates on a Riemannian manifold are local coordinates where the metric is conformal to the Euclidean metric. This means that in isothermal coordinates, the Riemannian metric locally has the form g = φ ( d x 1 2 + ⋯ + d x n 2 ) , {\displaystyle g=\varphi (dx_{1}^{2}+\cdots +dx_{n}^{2}),} where φ {\displaystyle \varphi } is a positive smooth function.
In mathematics, specifically in differential geometry, isothermal coordinates on a Riemannian manifold are local coordinates where the metric is conformal to the Euclidean metric. This means that in isothermal coordinates, the Riemannian metric locally has the form g = φ ( d x 1 2 + ⋯ + d x n 2 ) , {\displaystyle g=\varphi (dx_{1}^{2}+\cdots +dx_{n}^{2}),} where φ {\displaystyle \varphi } is a positive smooth function.
Source: Wikipedia "Isothermal coordinates" · CC BY-SA 4.0
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