Editing Conformal map (section)

===Riemannian geometry===
{{see also|Conformal geometry}}
In [[Riemannian geometry]], two [[Riemannian metric]]s <math>g</math> and <math>h</math> on a smooth manifold <math>M</math> are called '''conformally equivalent''' if <math> g = u h </math> for some positive function <math>u</math> on <math>M</math>. The function <math>u</math> is called the '''conformal factor'''.

A [[diffeomorphism]] between two Riemannian manifolds is called a '''conformal map''' if the pulled back metric is conformally equivalent to the original one.  For example, [[stereographic projection]] of a [[sphere]] onto the [[plane (mathematics)|plane]] augmented with a [[point at infinity]] is a conformal map.

One can also define a '''conformal structure''' on a smooth manifold, as a class of conformally equivalent [[Riemannian metric]]s.