Timeline for Invariance of a vector under parallel transport along an infinitesimal orthogonal loop
Current License: CC BY-SA 3.0
9 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Feb 10, 2018 at 22:00 | comment | added | Deane Yang | I was assuming the connection is the Levi-Civita connection which is torsion free. I don’t know happens if there’s torsion. My argument probably does not work in that case. | |
| Feb 10, 2018 at 21:55 | comment | added | Aegon | If the Ricci is a scalar multiple of the metric, does this imply that we also need torsion-free space? Since torsion is responsible for the anti-symmetric part of the connection, it would seem to me that is an additional requirement. Just confused about how torsion enters your calculation and if it would change anything in particular. | |
| Feb 5, 2018 at 6:34 | comment | added | Aegon | Thank you again, that helps! I think I understand from your calculation that the same should hold true even for curved space-time, although the example was done for d=3 curved space. Is this correct? Thank you again, I appreciate your help with this. | |
| Feb 4, 2018 at 21:56 | comment | added | Deane Yang | It's also explained here: projecteuclid.org/euclid.dmj/1077303336 | |
| Feb 4, 2018 at 21:55 | comment | added | Deane Yang | Here's an explanation: en.wikipedia.org/wiki/Ricci_decomposition | |
| Feb 4, 2018 at 21:30 | comment | added | Aegon | Thank you for that answer! Do you know of a good reference which shows the decomposition of the Reimann tensor as you've written it? I tried to show it using just the symmetries of the tensor but failed. | |
| Feb 4, 2018 at 21:09 | history | bounty ended | Aegon | ||
| Feb 3, 2018 at 6:35 | vote | accept | Aegon | ||
| Feb 3, 2018 at 0:55 | history | answered | Deane Yang | CC BY-SA 3.0 |