Timeline for Conformally flat manifold with zero scalar
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 18, 2016 at 5:25 | answer | added | Renato G. Bettiol | timeline score: 5 | |
| Jan 13, 2016 at 0:29 | comment | added | Robert Bryant | Do you want an explicit example or a proof that one exists? I think it is likely that there are such $(M^4,g)$, but I don't know how to make an explicit example. The idea for existence is to make a family of compact conformally flat $4$-manifolds by taking conformally flat connected sums of compact space forms, some with Yamabe energy $>0$ and some with Yamabe energy $<0$. Varying the parameters in the connected sum should make the Yamabe energy vary, so it should be possible to make one with zero Yamabe energy. Then, by Schoen, it will have a conformal metric with zero scalar curvature. | |
| Jan 12, 2016 at 19:23 | answer | added | Holonomia | timeline score: 1 | |
| Jan 12, 2016 at 16:01 | answer | added | Mikhail Katz | timeline score: 8 | |
| Jan 12, 2016 at 15:46 | review | First posts | |||
| Jan 12, 2016 at 15:50 | |||||
| Jan 12, 2016 at 15:41 | history | asked | Chris | CC BY-SA 3.0 |