Timeline for How submanifolds evolve under Ricci flow?
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
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| Nov 28, 2013 at 22:07 | answer | added | user41263 | timeline score: 8 | |
| Feb 8, 2013 at 1:55 | comment | added | Anton Petrunin | I am sure you know it, just in case: If your submanifold is a fixed set of some isometric action then it stay so under Ricci flow. | |
| Feb 8, 2013 at 1:16 | comment | added | Deane Yang | Or you could try to fix geodesic normal co-ordinates relative to the hypersurface. But then the co-ordinates also have to change in time as the metric changes. This sounds more difficult to me but you never know until you try. Anyway, answering questions like this usually require (at least for me) at lot of struggling with the calculations tried different ways. After you've tried all possible angles, what sometimes happens is that suddenly you realize there's an easy way to do it. The main goal is probably to figure out how the second fundamental form evolves. | |
| Feb 8, 2013 at 1:12 | comment | added | Deane Yang | I don't know if this has been studied before. You could email Ben Chow and ask him if he knows. Also, you could search "Ricci flow submanifold" on both arxiv and Mathscinet. If you find nothing, I suggest struggling with the calculations more and trying to different approaches. You could fix co-ordinates on $M$ and assume $N$ is given by the vanishing of the last $k$ co-ordinates, where $k$ is the codimension of $N$. I suggest first figuring out what happens to the second fundamental form for an arbitrary deformation of the metric. | |
| Feb 7, 2013 at 21:48 | history | asked | Renato G. Bettiol | CC BY-SA 3.0 |