Timeline for Finding an asymptotically flat manifold with ${\rm Ric}_{r\phi} = \frac{\sin\theta}{r^2}$
Current License: CC BY-SA 4.0
7 events
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| Apr 16, 2022 at 13:48 | history | edited | Laithy | CC BY-SA 4.0 |
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| Apr 16, 2022 at 2:28 | comment | added | Vitali Kapovitch | ah, ok, sorry, I thought subindices were coordinates of a point. | |
| Apr 16, 2022 at 2:27 | comment | added | Laithy | I am not making any other assumptions about the rest of the Ricci components. So the Ricci curvature need not be (and cannot be) pointwise constant. | |
| Apr 16, 2022 at 2:23 | comment | added | Laithy | I mean the function ${\rm Ric}(\frac{\partial}{\partial r}, \frac{\partial}{\partial \phi})$ on $\mathbb{R}^3\setminus B_1$ is the function $\frac{\sin \theta}{r^2}$. | |
| Apr 16, 2022 at 2:20 | comment | added | Vitali Kapovitch | what exactly do you mean by the equality ${\rm Ric}_{r\phi} = \frac{\sin\theta}{r^2}$? that Ricci curvature is pointwise constant? then the answer is No by Schur's Lemma. | |
| Apr 15, 2022 at 21:38 | history | edited | Laithy | CC BY-SA 4.0 |
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| Apr 15, 2022 at 21:11 | history | asked | Laithy | CC BY-SA 4.0 |