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conformally flat manifold

A (pseudo-)Riemannian manifold is conformally flat if each point has a neighborhood that can be mapped to flat space by a conformal transformation. In practice, the metric g of the manifold M has to be conformal to the flat metric η, i.e., the geodesics maintain in all points of M the angles by moving from one to the other, as well as keeping the null geodesics unchanged, that means exists a function λ(x) such that g(x) = λ²(x).η, where λ(x) is known as the conformal factor and x is a point on the manifold. (Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/wiki/Conformally_flat_manifold)

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