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--- conformal_change_formulae [2022/08/31 13:43] – spencer
+++ conformal_change_formulae [2022/08/31 13:46] (current) – spencer
@@ Line 9: / Line 9: @@
 Thus at $p$,
 \begin{align*}
-\mathrm{vol}(\widetilde{g}) &= \sqrt{(e^{2\phi})^n} \mathrm{d}x^1 \wedge \cdots \wedge \mathrm{d}x^n \\
+\mathrm{vol}(\widetilde{g}) &= \sqrt{\mathrm{det} \widetilde{g}}\, \mathrm{d}x^1 \wedge \cdots \wedge \mathrm{d}x^n \\
+&= \sqrt{(e^{2\phi})^n} \,\mathrm{d}x^1 \wedge \cdots \wedge \mathrm{d}x^n \\
 &= e^{\phi n} \mathrm{vol}(g).
 \end{align*}