Timeline for Torsion and submanifolds [closed]
Current License: CC BY-SA 3.0
17 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jul 18, 2013 at 23:34 | comment | added | Oliver Jones | @Ramiro: Since people want to vote the question down, how do I go about modifying it? It's not a big change by the way. | |
| Jul 18, 2013 at 22:56 | comment | added | Ramiro de la Vega | Oliver, you shouldn't accept an answer and then change the question. | |
| Jul 18, 2013 at 21:50 | review | Reopen votes | |||
| Jul 19, 2013 at 6:07 | |||||
| Jul 18, 2013 at 21:33 | history | edited | Oliver Jones | CC BY-SA 3.0 |
Modification of question.
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| S Jul 18, 2013 at 13:23 | history | unlocked | CommunityBot | ||
| S Jul 18, 2013 at 13:23 | history | locked | CommunityBot | ||
| S Jul 18, 2013 at 13:23 | history | closed |
Ryan Budney Daniel Moskovich Willie Wong Todd Trimble Peter Michor |
Not suitable for this site | |
| Jul 18, 2013 at 8:00 | comment | added | Oliver Jones | @Peter: So it's the Lie bracket that respects vectors tangent to $N$. Thanks, that clears things up. | |
| Jul 18, 2013 at 7:41 | vote | accept | Oliver Jones | ||
| Jul 18, 2013 at 7:09 | review | Close votes | |||
| Jul 18, 2013 at 13:23 | |||||
| Jul 18, 2013 at 6:45 | answer | added | Peter Michor | timeline score: 3 | |
| Jul 18, 2013 at 6:34 | comment | added | Peter Michor | @Oliver Jones: Since the Lie bracket respects vector fields which are tangent to $N$, and the torsion does not (in general), so also $\nabla_XY-\nabla_YX$ does not. | |
| Jul 18, 2013 at 2:49 | comment | added | Oliver Jones | @Mariano: Good point! But what about the term $\nabla_XY-\nabla_YX$? | |
| Jul 18, 2013 at 1:14 | comment | added | Mariano Suárez-Álvarez | Pick a point $p$ in $M$ and any subspace $S\subseteq T_pM$. There is a submanifold $N$ of $M$ such that $p\in N$ and $T_pN=S$. If what you want were true, then the torsion tensor would preserve all subspaces of $T_pM$! | |
| Jul 18, 2013 at 1:12 | comment | added | Oliver Jones | @Robert: Is it the case that $\nabla_XY-\nabla_YX$ lies in the tangent space of $N$? | |
| Jul 18, 2013 at 0:00 | comment | added | Robert Bryant | There's no reason for this to be true, and I'm sure that, for the generic submanifold $N$ of dimension 2 or more (if the dimension of $M$ is at least $3$ and the torsion doesn't satisfy some very special identity) then it won't be true. | |
| Jul 17, 2013 at 23:40 | history | asked | Oliver Jones | CC BY-SA 3.0 |