 Isothermal coordinates

Coordinates $(u,v)$ on an immersed surface are isothermal when the first fundamental form is ${\lambda }^2(d{u}^2+d{v}^2)$ for a positive function $\lambda$.

Isothermal coordinates refer to a specific type of coordinate system used in differential geometry, particularly in the study of surfaces and Riemannian manifolds. These coordinates are characterized by their property that the metric induced on the surface can be expressed in a particularly simple form.