2023-12-16   96560

The Curvature of a Conformally Flat Manifold

The standard N-dimensional sphere is an example of a smooth manifold that is curved but conformally flat. This article calculates the Ricci tensor for an arbitrary N-dimensional conformally flat manifold with arbitrary signature and then shows that the result simplifies as expected when the space is maximally symmetric. The result is used to show that the scalar curvature for a standard sphere of radius σ is N(N-1)/σ^2.

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www.cphysics.org updated 2024-07-11