Timeline for Does the Lie bracket of a certain pair of vector fields vanish?
Current License: CC BY-SA 4.0
9 events
| when toggle format | what | by | license | comment | |
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| Jan 8, 2023 at 16:52 | answer | added | Deane Yang | timeline score: 2 | |
| Jan 8, 2023 at 7:10 | comment | added | Deane Yang | I took a look at page 283 of the paper, and indeed what I said above is what they mean. I suggest reading about Jacobi fields in any standard textbook on Riemannian geometry and working out your own version of the calculation. If I have time, I’ll write an answer. | |
| Jan 8, 2023 at 1:47 | history | edited | LSpice | CC BY-SA 4.0 |
Link to article
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| Jan 7, 2023 at 17:31 | history | edited | Steve | CC BY-SA 4.0 |
added 129 characters in body
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| Jan 6, 2023 at 15:22 | comment | added | Deane Yang | By definition, a Jacobi field is the restriction of a vector field obtained by differentiating a 1-parameter family of geodesics with respect to the parameter. The Lie bracket of that vector field with the vector field of velocity vectors of the geodesics vanishes. Perhaps that’s what the authors are using. | |
| Jan 6, 2023 at 10:00 | comment | added | Ben McKay | I don't understand the question .The vector fields are only defined along curves, but $J$ is not tangent to the curve. The Lie bracket is the derivative as we flow one vector field along the flow of the other (the fishing derivative). But we don't have flows defined. So what is the meaning of Lie derivative here? | |
| Jan 6, 2023 at 0:27 | history | edited | YCor | CC BY-SA 4.0 |
moved (poorly pasted) citation at the end, formatting
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| S Jan 6, 2023 at 0:05 | review | First questions | |||
| Jan 6, 2023 at 0:12 | |||||
| S Jan 6, 2023 at 0:05 | history | asked | Steve | CC BY-SA 4.0 |