Timeline for Does the Lie bracket of a certain pair of vector fields vanish?
Current License: CC BY-SA 4.0
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| when toggle format | what | by | license | comment | |
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| Jan 9, 2023 at 23:07 | comment | added | Deane Yang | You should prove that yourself. | |
| Jan 9, 2023 at 22:50 | comment | added | Steve | Thanks for the explanation. I knew that you can get a Jacobi field by differentiating a family of geodesics (w.r.t. the appropriate parameter). I.e., that operation yields a vector field satisfying the Jacobi equation (which I take to be the definition of a Jacobi field). I was unsure whether the converse is true, i.e., if you have a vector field satisfying the Jacobi equation then there exists a family of geodesics, etc. I guess the answer is "yes". | |
| Jan 8, 2023 at 16:52 | history | answered | Deane Yang | CC BY-SA 4.0 |