Timeline for Curvature collineation and the Killing identity
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
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| Jul 22, 2020 at 21:39 | comment | added | Willie Wong | Note that in dimension 5, things start looking better for $\Upsilon$: the domain is 75 dimensional, while the image is $\binom{5}{2} \binom{5}{3} = 100$ dimensional (we note the image is also antisymmetric in the $d$ and $e$ indices), so we have hope. | |
| Jul 22, 2020 at 21:33 | history | edited | Willie Wong | CC BY-SA 4.0 |
fixed minor typos
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| Jul 22, 2020 at 21:29 | comment | added | Willie Wong | Some people take $R_{ijkl} X^l = [\nabla_i, \nabla_j ]X_k$, some people define it to be the negative. I used in this computation the convention indicated in this comment, you are using the opposite one. So my version of the "Killing identity" is off from yours by a minus sign. | |
| Jul 22, 2020 at 20:32 | vote | accept | Spoilt Milk | ||
| Jul 22, 2020 at 17:27 | comment | added | Spoilt Milk | Shouldn't the Riemann tensor terms be $R_{splm} + R_{smpl} + R_{slpm}$ so that using $R_{s[plm]} = 0$ would give the result mentioned? You have mentioned that your sign convention is different, but I don't get it. Could you please clarify this. Thanks for the answer. | |
| Jul 22, 2020 at 15:45 | history | edited | Willie Wong | CC BY-SA 4.0 |
added 283 characters in body
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| Jul 22, 2020 at 15:40 | history | answered | Willie Wong | CC BY-SA 4.0 |