Timeline for Let $M$ be a manifold with a conformal structure and a volume measure. How can one reconstruct a metric on $M$ from this data in a geometric way?
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Aug 26, 2023 at 15:39 | answer | added | Ben McKay | timeline score: 1 | |
| Aug 26, 2023 at 11:07 | answer | added | Ben Whale | timeline score: 2 | |
| May 18, 2023 at 12:15 | comment | added | Deane Yang | @RBega2’s comment leads me to believe that you might want to consider the appropriate frame bundles (more torsors). | |
| May 18, 2023 at 2:57 | answer | added | Ian Agol | timeline score: 2 | |
| May 17, 2023 at 22:57 | comment | added | RBega2 | Thinking about it some more I probably the correct framework is of G-structures. The conformal structure is then a $G$ structure modeled on conformal matrices $Co(n)$. For an orientable manifold the structure group for volume forms is $SL(n)$ (this can be extended to the non-orientable case in a straightforward way). The map you describe initially should come from the inclusion $O(n)\subset Co(n)$. I would guess what you are after comes from $Co(n)\cap SL(n)=SO(n)$. | |
| May 17, 2023 at 22:17 | comment | added | RBega2 | I'm not totally sure what sort of answer you are looking for, but I would guess the first place to start looking is in the tractor calculus | |
| May 17, 2023 at 20:18 | history | asked | Tim Campion | CC BY-SA 4.0 |