Timeline for For a 1-parameter family of metrics, how do we compute the derivative of the intrinsic geometrical objects like curvature, Hessian, etc
Current License: CC BY-SA 4.0
10 events
| when toggle format | what | by | license | comment | |
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| Dec 8, 2020 at 3:04 | comment | added | Laithy | Yes they are useful. Check section 2.3: Deformation of geometric quantities as the metric is deformed. homepages.warwick.ac.uk/~maseq/topping_RF_mar06.pdf | |
| Dec 8, 2020 at 2:37 | comment | added | Otis Chodosh | Topping's lecture notes on Ricci flow are useful for this sort of thing (I dont think they have all the calculations you want though). | |
| Dec 8, 2020 at 1:55 | comment | added | Laithy | I did the calculations for some of them myself. I am not too confident they are correct. I can share them if anyone is interested. For $\Delta_{g(t)}u(t)$, I really didn't find a nice form for it, and also didn't find it in Ricci and mean curvature flow books. | |
| Dec 8, 2020 at 1:53 | comment | added | Laithy | Thanks a lot. This helped: maths-people.anu.edu.au/~andrews/book.pdf. | |
| Dec 7, 2020 at 14:05 | comment | added | Deane Yang | The calculations for the Ricci and mean curvature flows provide good guides on how to do the calculations. | |
| Dec 7, 2020 at 12:30 | comment | added | Malkoun | ok, sorry about that. I have a small remark, that $\tilde{g}$ need not be positive-definite in general. | |
| Dec 7, 2020 at 6:27 | comment | added | Laithy | Thank you. I had a look at Besse and some books on Ricci flow. I couldn't find the variation of the second fundamental form and $\Delta_{g(t)}u(t)$. | |
| Dec 7, 2020 at 5:47 | review | Close votes | |||
| Dec 20, 2020 at 8:04 | |||||
| Dec 7, 2020 at 3:14 | comment | added | Malkoun | if I remember correctly (though I could be wrong), you may be able to find these formulas perhaps in Besse's "Einstein manifolds". If not, then you would probably find them in a textbook on the Ricci flow. | |
| Dec 7, 2020 at 2:43 | history | asked | Laithy | CC BY-SA 4.0 |