Conformally flat manifold
A 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 be a pseudo-Riemannian manifold. Then 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 is flat. The function f need not be defined on all of M.
Some authors use locally conformally flat to describe the above notion and reserve conformally flat for the case in which the function f is defined on all of M.Examples
