Timeline for Curvature collineation and the Killing identity
Current License: CC BY-SA 4.0
12 events
| when toggle format | what | by | license | comment | |
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| Jul 22, 2020 at 20:32 | vote | accept | Spoilt Milk | ||
| Jul 22, 2020 at 15:40 | answer | added | Willie Wong | timeline score: 2 | |
| Jul 22, 2020 at 13:23 | comment | added | Deane Yang | No, that's not right. The Killing identity does not follow from the collineation equation. | |
| Jul 22, 2020 at 12:59 | comment | added | Deane Yang | If the metric is flat, the vector field need not satisfy the identity. | |
| Jul 22, 2020 at 9:59 | history | edited | Spoilt Milk | CC BY-SA 4.0 |
Added my attempt to solution
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| Jul 22, 2020 at 4:35 | history | edited | Spoilt Milk | CC BY-SA 4.0 |
made statement more precise.
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| Jul 22, 2020 at 4:30 | comment | added | Spoilt Milk | @DeaneYang Yeah $K=X$ in this case, and yes this does work for any smooth vector field. But if $X$ is a Killing field and the $(0,4)$ covariant tensor is the Riemann tensor, curvature collineation holds and this should simplify to the Killing identity (right?) | |
| Jul 21, 2020 at 22:39 | history | edited | YCor | CC BY-SA 4.0 |
removed capitals from title
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| Jul 21, 2020 at 21:32 | comment | added | Deane Yang | Notice that this can't work in general. In particular, if the metric is flat, then the equation you've written holds for any vector field and not just Killing fields. | |
| Jul 21, 2020 at 21:31 | comment | added | Deane Yang | In your formulas, is $K = X$? | |
| Jul 21, 2020 at 19:00 | history | edited | Spoilt Milk |
edited tags
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| Jul 21, 2020 at 17:50 | history | asked | Spoilt Milk | CC BY-SA 4.0 |