Scalar curvature under conformal rescaling
= Scalar curvature under conformal rescaling
{title2=$\widetilde R=e^{-2\omega}[R-2(N-1)\Delta_g\omega-(N-1)(N-2)|\nabla\omega|_g^2]$}
In dimension $N$, the <conformal rescaling of a Riemannian metric> $\widetilde g=e^{2\omega}g$ changes the <Ricci scalar> by the displayed formula. In two dimensions the gradient-square term vanishes; for a flat base metric, $\widetilde R=-2e^{-2\omega}\Delta\omega$.