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Use this for questions pertaining to curvature of manifolds. Does not need to be specific to general relativity, but also for curvature of e.g. a Calabi-Yau manifold.

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Evaluating curvature given a metric

A book I'm reading suggests checking if a metric describes a curved space by calculating $$ R = \lim_{\small{radius} \to 0} \frac 6 {(\hbox{radius})^2} \bigg(1 - \frac {\hbox{circumference}} {2\pi \ …
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