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# Conformal equivalence

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.

Ramanan, S. (2005), Global Calculus, American Mathematical Society, p. 221, ISBN 9780821872406.

Undergraduate Texts in Mathematics

Graduate Studies in Mathematics

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