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Stupid question about the Ricci Flow...

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OK, I have a stupid question, but if one had the equation:

[math]\delta (g^{ij}(t+\delta t))/\delta (g^{ij}(t))[/math]

wouldn't that be equivalent to

[math]\partial_{t} g^{ij}(t)[/math]

and thus definitionally

[math] -R^{ij} [/math]

via the definition of the Ricci flow?

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