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.