Conformally flat manifold
（重定向自Conformally flat）
A (pseudo-)Riemannian manifold is conformally flat if each point has a neighborhood that can be mapped to flat space by a conformal transformation.
More formally, let (M, g) be a pseudo-Riemannian manifold. Then (M, g) is conformally flat if for each point x in M, there exists a neighborhood U of x and a smooth function f defined on U such that (U, eg) is flat (i.e. the curvature of eg vanishes on U). The function f need not be defined on all of M.