In mathematics, conformal geometry is the study of the set of angle-preserving (conformal) transformations on a space. In two real dimensions, conformal geometry is precisely the geometry of Riemann surfaces. In more than two dimensions, conformal geometry may refer either to the study of conformal transformations of "flat" spaces (such as Euclidean spaces or spheres), or, more commonly, to the study of conformal manifolds which are Riemannian or pseudo-Riemannian manifolds with a class of metrics defined up to scale. Study of the flat structures is sometimes termed Möbius geometry, and is a type of Klein geometry.
Read more about Conformal Geometry: Conformal Manifolds, Möbius Geometry
Famous quotes containing the word geometry:
“The geometry of landscape and situation seems to create its own systems of time, the sense of a dynamic element which is cinematising the events of the canvas, translating a posture or ceremony into dynamic terms. The greatest movie of the 20th century is the Mona Lisa, just as the greatest novel is Gray’s Anatomy.”
—J.G. (James Graham)