conformal metric

Definition

On a smooth manifold $M$, with two Riemannian metrics $g,\tilde{g}$, $\tilde{g}$ is called conformal to $g$ if

$$\tilde{g}={\rho }^2\cdot g\rho >0$$

for some smooth function $\rho$.

Uses

Conformal metrics preserve angles (but not lengths).