Timeline for Reference for parallel transport around loop and its relation to curvature
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jul 27, 2021 at 18:55 | comment | added | Ziad H. Muhammad | @Qfwfq I want to know this too. my idea is that it doesn't matter the curve as long as the parallel transport map of the connection is the one used. but I'm not sure. | |
| Jun 15, 2017 at 22:24 | comment | added | Qfwfq | Are you sure the formula you report is correct? I would have thought that, in the limit expression for the curvature of $\nabla$, $P_t^X$ were the parallel transport along the geodesic (with respect to $\nabla$) along the direction $X\in T_p M$ at time $t$, not the flow of a vector field extending $X$ locally. Or maybe it's the same? | |
| Jun 15, 2017 at 21:20 | comment | added | Urs Schreiber | Also lemma 3.5 in "Smooth functors vs Differential Forms" arxiv.org/abs/0802.0663 | |
| Jun 15, 2017 at 20:54 | answer | added | Mizar | timeline score: 6 | |
| Jun 15, 2017 at 13:07 | comment | added | Deane Yang | You might be able to adapt the calculation here: deaneyang.com/papers/holonomy.pdf to get what you want. | |
| Jun 15, 2017 at 10:05 | history | asked | Bence Racskó | CC BY-SA 3.0 |