Timeline for Range of divergence operator on the space of traceless symmetric $(0,2)$ tensors; conformal vector fields on an arbitrary metric on $S^2$
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
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| Feb 22, 2021 at 17:53 | comment | added | Laithy | OH! that was what's wrong! Thank you @WillieWong Do you know precisely what is the family of $f$ such that $\gamma = f^2 \gamma_0$? Is that a 3-parameter family of functions? | |
| Feb 22, 2021 at 17:46 | comment | added | Willie Wong | If you have a smooth metric on $\mathbb{S}^2$, it cannot have (globally) negative curvature by Gauss-Bonnet. | |
| Feb 22, 2021 at 17:29 | comment | added | Laithy | Oh so my calculation at the end was correct. I thought if the metric has negative curvature, then it doesn't admit CK vector fields. That must be wrong then. Thank you. | |
| Feb 22, 2021 at 17:25 | comment | added | Ben McKay | Conformal Killing vector fields are the same for any two conformal metrics. Any two metrics on the sphere are conformal up to diffeomorphism (by the uniformization theorem for Riemann surfaces). So the conformal Killing fields are identified by that diffeomorphism. | |
| Feb 22, 2021 at 17:19 | history | asked | Laithy | CC BY-SA 4.0 |