conformal_change_formulae
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| conformal_change_formulae [2022/08/31 13:46] – spencer | conformal_change_formulae [2022/08/31 13:46] (current) – spencer | ||
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| Thus at $p$, | Thus at $p$, | ||
| \begin{align*} | \begin{align*} | ||
| - | \mathrm{vol}(\widetilde{g}) &= \sqrt{\mathrm{det} \widetilde{g}} \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 \\ | + | &= \sqrt{(e^{2\phi})^n} |
| &= e^{\phi n} \mathrm{vol}(g). | &= e^{\phi n} \mathrm{vol}(g). | ||
| \end{align*} | \end{align*} | ||
conformal_change_formulae.1661967983.txt.gz · Last modified: by spencer