Timeline for harmonic curvature versus Einstein metric
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Oct 28, 2013 at 16:25 | comment | added | Viktor Bundle | Deane: Dan has the right idea. dRic is $D_i R_{jk} = D_j R_{ik}$. | |
| Oct 28, 2013 at 16:23 | vote | accept | Viktor Bundle | ||
| Oct 27, 2013 at 23:21 | answer | added | Robert Bryant | timeline score: 8 | |
| Oct 27, 2013 at 18:01 | comment | added | Dan Fox | I think by $dRic = 0$ the poster means $D_{i}R_{jk} = D_{j}R_{ik}$, since (Bianchi identities) this is equivalent to $D^{p}R_{ijkp} = 0$, which is sometimes called "harmonic curvature". | |
| Oct 27, 2013 at 16:57 | comment | added | Deane Yang | I find this question confusing. What does "dRic" mean? Is it the full covariant derivative of Ricci? If so, doesn't dRic = 0 imply harmonic curvature? Or are you asking a topological question: Does there exist a manifold that has metrics with harmonic curvature but none that are Einstein? | |
| Oct 27, 2013 at 14:37 | history | asked | Viktor Bundle | CC BY-SA 3.0 |