Conformal equivalence
From HandWiki
Redirect page
Redirect to:
Stereographic projection is a conformal equivalence between a portion of the sphere (with its standard metric) and the plane with the metric [math]\displaystyle{ \frac{4}{(1 + X^2 + Y^2)^2} \; ( dX^2 + dY^2) }[/math].
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.[1] 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.[2] Conformal equivalence is an equivalence relation on geometries or on Riemannian metrics.
See also
- conformal geometry
- biholomorphic equivalence
- AdS/CFT correspondence
References
- ↑ Conway, John B. (1995), Functions of One Complex Variable II, Graduate Texts in Mathematics, 159, Springer, p. 29, ISBN 9780387944609, https://books.google.com/books?id=JN0hz3qO1eMC&pg=PA29.
- ↑ Ramanan, S. (2005), Global Calculus, American Mathematical Society, p. 221, ISBN 9780821872406, https://books.google.com/books?id=1INoRKtgndcC&pg=PA221.
