Timeline for How to solve the system of PDEs defining Killing vectors
Current License: CC BY-SA 3.0
8 events
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| Feb 7, 2017 at 22:06 | vote | accept | Stefan Vasilev | ||
| Feb 7, 2017 at 22:06 | comment | added | Stefan Vasilev | You are right about the index, but this was a typo only in the post (I edited it). Otherwise, the system is obviously trivial once we know that $X$ is Killing. I assume the idea is to first arrive at the curvature condition to illustrate what the extreme case is, and apply the symmetry $X_{ij} = - X_{ji}$ afterwards. | |
| Feb 7, 2017 at 21:58 | history | edited | Stefan Vasilev | CC BY-SA 3.0 |
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| Feb 7, 2017 at 19:42 | answer | added | José Figueroa-O'Farrill | timeline score: 8 | |
| Feb 7, 2017 at 19:16 | comment | added | Willie Wong | You probably copied your equation wrong: for the equation with Riemann, did you want the final factor to be $X^p$ instead? Also, the way the question is written is strange: if you assume $X_{ij} = - X_{ji}$, then by definition the deformation tensor for $X$ vanishes, which implies that $X$ is Killing. When that happens the equation on $\nabla_k X^j_i$ is simply Jacobi's equation for Killing vector fields. In other words, the assumption that $X_{ij} = -X_{ji}$ implies the rest of the system, and I can't imagine why the exercise is formulated that way. | |
| Feb 7, 2017 at 19:04 | history | edited | Willie Wong |
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| Feb 7, 2017 at 16:22 | review | First posts | |||
| Feb 7, 2017 at 16:24 | |||||
| Feb 7, 2017 at 16:19 | history | asked | Stefan Vasilev | CC BY-SA 3.0 |