Editing Conformal geometry (section)

{{Short description|Study of angle-preserving  transformations of a geometric space}}
In [[mathematics]], '''conformal geometry''' is the study of the set of angle-preserving ([[conformal map|conformal]]) transformations on a space.

In a real two dimensional space, conformal geometry is precisely the geometry of [[Riemann surfaces]]. In space higher than two dimensions, conformal geometry may refer either to the study of [[conformal mapping|conformal transformations]] of what are called "flat spaces" (such as [[Euclidean space]]s or [[n-sphere|spheres]]), or to the study of '''conformal manifolds''' which are [[Riemannian manifold|Riemannian]] or [[pseudo-Riemannian manifold]]s with a class of [[metric tensor|metrics]] that are defined up to scale. Study of the flat structures is sometimes termed '''Möbius geometry''', and is a type of [[Klein geometry]].