Conformal equivalence

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• Conformal geometry

Stereographic projection is a conformal equivalence between a portion of the sphere (with its standard metric) and the plane with the metric $\frac{4}{(1+X^2+Y^2{)}^2}(d{X}^2+d{Y}^2)$.

In mathematics and theoretical physics, two geometries are conformally equivalent if there exists a conformal transformation (an angle-preserving transformation) that maps one geometry to the other one. More generally, two Riemannian metrics on a manifold M are conformally equivalent if one is obtained from the other by multiplication by a positive function on M. Conformal equivalence is an equivalence relation on geometries or on Riemannian metrics.

See also

• conformal geometry
• biholomorphic equivalence
• AdS/CFT correspondence