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I started learning about Ricci flow recently, which is always given as $$ \frac{\partial g}{\partial t}=-2\textrm{Ric}. $$ It would seem more natural to me to define Ricci flow instead by the equation $$ \frac{\partial g}{\partial t}=-\textrm{Ric}, $$ which omits the $2$. The only real difference in behavior between this flow and Ricci flow is that this one flows at half the rate. Wikipedia claims that the choice of $2$ in the equation is an arbitrary convention, but this is hard for me to stomach, since conventions in math are almost always motivated by something. Is there a good reason that Ricci flow is defined the way it is, or is the convention really arbitrary?

subrosar
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    Because we prefer that the equation for the metric to look like $$\partial_tg = \Delta g + \ldots $$ – Deane Jul 19 '21 at 04:12
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    So I guess it's the same question as whether "the heat equation" is $\partial_t u = \Delta u$ or $\partial_t u = \frac{1}{2} \Delta u$. Which maybe is the same question as "are you an analyst or a probabilist?". – Nate Eldredge Aug 02 '21 at 15:51

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