Timeline for Principal Symbol for the Ricci-DeTurck Flow
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Feb 17, 2019 at 18:43 | comment | added | Panagiotis Konstantis | That would have been my guess too. | |
| Feb 17, 2019 at 16:41 | comment | added | Hollis Williams | I've thought about it and I think that the fact that Topping has it with a $T$ rather than a $h$ must be a typo, as it changes back to $h$ when he linearizes the operator, then the implication comes from definition of the Lie derivative. | |
| Feb 16, 2019 at 15:35 | comment | added | Hollis Williams | Also, in this expression with the Lie derivatives the term on the right-hand side involves a second derivative of $h$ and the dots indicate terms which contain $h$ and its first derivative. | |
| Feb 16, 2019 at 15:26 | comment | added | Hollis Williams | Hi this is correct, I was working from Topping's lecture notes on Ricci flow. Also, once we have the desired expression he says that this implies that $\frac{\partial}{\partial t} L_{(T^{-1} \delta G(T))^{\#}}g = -L_{(\delta G(T))^{\#}} + ... $ where $L$ is the Lie derivative. So, it has to be a sharp as it needs to be a vector field in the direction of which the Lie derivative acts, but why is it $\delta G(T)$ and not $\delta G(h)$? | |
| Feb 16, 2019 at 13:44 | vote | accept | Hollis Williams | ||
| Feb 15, 2019 at 21:08 | history | answered | Panagiotis Konstantis | CC BY-SA 4.0 |