Timeline for Ricci flow preserves holonomy
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
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| Aug 13, 2016 at 13:45 | answer | added | Robert Bryant | timeline score: 12 | |
| Aug 8, 2016 at 15:34 | comment | added | YangMills | For your last question, you can also prove directly that the Kahler-Ricci flow has a solution for short time, by writing it as a parabolic scalar complex Monge-Ampere equation. By construction, the solution is Kahler as long as it exists. But it also solves the Riemannian Ricci flow, so by uniqueness of Ricci flow solutions you conclude that the Ricci flow preserves Kahler. | |
| Aug 8, 2016 at 12:44 | review | Close votes | |||
| Aug 8, 2016 at 18:35 | |||||
| Aug 8, 2016 at 12:24 | comment | added | Anton Petrunin | Let $H$ be the holonomy group and $\mathfrak{h}$ be the corresponding subalgebra in $\mathfrak{so}(n)$. The algebra $\mathfrak{so}(n)$ can be identified with the space of bivector $\Lambda^2(T)$. Note that $\mathfrak{h}$ forms a parallel distribution in and the curvature operator has values in $\mathfrak{h}$. It remains to apply the formula for curvature evolution. | |
| Aug 8, 2016 at 12:23 | comment | added | Igor Belegradek | Do you find arxiv.org/abs/1105.3722 and references therein insufficient? | |
| Aug 8, 2016 at 10:45 | history | asked | Bingo | CC BY-SA 3.0 |