Timeline for What is torsion in differential geometry intuitively?
Current License: CC BY-SA 3.0
13 events
| when toggle format | what | by | license | comment | |
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| Jul 27, 2021 at 16:18 | comment | added | Ziad H. Muhammad | @MichaelWeiss this is really what got me to like DG. it can get very abstract but the main reasoning behind most of the ideas is still "geometric". which makes it tasteful at least to my liking. | |
| Apr 9, 2018 at 17:30 | comment | added | Michael Weiss | @asv Yes, that's how you do it for a formal definition. In other words, you compare parallel transport with Lie dragging. MTW discuss this (briefly) in their text; also, if you want a really thorough rigorous discussion of torsion, other books are a better bet. | |
| Apr 8, 2018 at 18:09 | comment | added | asv | Thank you for addendum. Maybe we can move $ϵu||$, $ϵv||$ to point $P(0)$ by the flux of $u$ and $v$ | |
| Mar 18, 2018 at 14:46 | comment | added | Michael Weiss | @asv Valid point. I thought it merited adding an addendum to my original answer. | |
| Mar 18, 2018 at 14:43 | history | edited | Michael Weiss | CC BY-SA 3.0 |
fixed a typo
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| Mar 17, 2018 at 14:52 | comment | added | asv | In image $\epsilon^2 τ(u_0,v_0) = \epsilon u_{||} - \epsilon v_{||} $, I don't understand how we can make the difference between two vectors which are in different tangent spaces. | |
| Nov 9, 2017 at 15:27 | comment | added | TheQuantumMan | Excellent. Thank you | |
| Nov 3, 2017 at 19:37 | comment | added | Michael Weiss | If you want to see a diagram for Cartan's spiral staircase, google that phrase; you'll find an arXiv article by Hehl and Obukhov; look at Fig. 13 (p.22). (Incidentally, they have a figure much like my second diagram; I only discovered this paper after I'd posted my answer. I haven't seen my 2d example elsewhere to date.) | |
| Nov 3, 2017 at 19:32 | comment | added | Michael Weiss | The common theme is the failure of quadrilaterals to close under parallel transport. One of the other answers (anonymous, near the top) gives the example of Cartan's spiral staircase; this is a 3d example, so you have more flexibility. I constructed my example when I was wondering if you could have non-zero torsion in 2d. The answer is yes, as you can see. | |
| Nov 2, 2017 at 23:38 | comment | added | TheQuantumMan | Dear Michael, do you know how to go from your explanation to the explanation of frame-rotation? In particular, there are answers that say(or give examples showing that) non-zero torsion means that vectors perpendicular to the tangent vector of a curve will rotate around it. How could the two explanations be connected> | |
| May 20, 2017 at 17:38 | history | edited | Michael Weiss | CC BY-SA 3.0 |
increased the resolution of the 2nd figured; fixed a mis-statement; added comment about zero curvature
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| May 20, 2017 at 15:49 | history | edited | Michael Weiss | CC BY-SA 3.0 |
deleted 98 characters in body
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| May 20, 2017 at 15:30 | history | answered | Michael Weiss | CC BY-SA 3.0 |