Conformal rescaling of a Riemannian metric
= Conformal rescaling of a Riemannian metric
{title2=$\widetilde g=e^{2\omega}g$}
A conformal rescaling multiplies a Riemannian metric by a positive scalar function. It preserves angles while changing lengths and volumes; in two dimensions, $\widetilde g=e^{2\omega}g$ gives $\Delta_{\widetilde g}=e^{-2\omega}\Delta_g$ on scalar functions.