Conformal Transformations in Riemannian Geometry

In this essay, we show our readers the transformations of the Christoffel symbols, Riemann tensor, Ricci tensor, Ricci scalar, Einstein tensor, as well as the invariance of the Weyl tensor, in response to a conformal transformation of the metric tensor: $$g^{\mu\nu} \rightarrow \tilde{g}^{\mu\nu} \equiv g^{\mu\nu} e^{2w},$$ where \(w\) is a scalar. One can find all the detailed computations in Conformal Transformations in Riemannian Geometry. It is free to read the document available, but please do not forward or distribute it to anyone. Thank you!

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