Conformally Tlat Manifold
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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. 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, e2fg) is flat (i.e. the curvature of e2fg vanishes on U). The function f need not be defined on all of M. Some authors us...
Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. 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, e2fg) is flat (i.e. the curvature of e2fg vanishes on U). 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.
