Timeline for What is torsion in differential geometry intuitively?
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 2, 2017 at 23:36 | comment | added | TheQuantumMan | Dear Bruce, could you please explain to me what you mean by metric and geodesic preserving? For example, metric preserving means compatible with the metric? If so, then what is the analog of geodesic preserving? | |
| Jul 1, 2015 at 16:26 | comment | added | Bruce Bartlett | See also these notes. | |
| Jul 1, 2015 at 1:09 | comment | added | Bruce Bartlett | Indeed, the picture is more complicated than I initially thought. I think these notes clears up things. Corollary 2.1 of that paper shows that if a connection is metric and geodesic-preserving (I had not appreciated the distinction), then it must have only skew-symmetric torsion, which means the dimension must be greater than 2. So it seems I was talking about connections which are both compatible with the metric and preserve geodesics. (Still amazed that these notions are different!) | |
| Jun 1, 2015 at 21:35 | comment | added | Holonomia | Dear Bruce, I do not understand your picture in dimension $n=2$. Namely, $v(t)$ remains constant as you said. But in dimension $n=2$ there are just one orthogonal $e_2(t)$ (up to $\pm$ sign of course). Then it follows that also $e_2(t)$ remains constant. So I do not see that the frame is "rotating" around the axis $v$. Namely, it seems to me that your picture imply (in dimension 2) that any compatible connection is torsion free hence the Levi-Civita connection. But this is not true. | |
| Nov 18, 2013 at 11:48 | comment | added | Marc Nieper-Wißkirchen | Your geometric picture is right. | |
| Sep 21, 2013 at 22:17 | history | answered | Bruce Bartlett | CC BY-SA 3.0 |