Timeline for A name for a pseudo-Riemannian manifold that admits no nonzero null vectors
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
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| Feb 7, 2023 at 11:12 | vote | accept | Martim Pereir | ||
| Oct 9, 2021 at 12:03 | comment | added | Robert Bryant | You are asking about 'nonvanishing null vector fields', not 'nonzero null vectors', and your attempt of '[question][1]' for a link to some other reference question is not working, so we can't see that. $$ $$An explicit example is to consider the torus $T = R/(\pi Z)\times R/(\pi Z)$ and the metric $g = \cos 2x\, (2\,dx\,dy) + \sin 2x\,(dx^2-dy^2)$, which has no nonvanishing null vector field, $X= a\,\partial_x + b\,\partial_y$ because such an $X$ would have $a$ and $b$ be $\pi$-periodic and satisfy either $a\cos x + b\sin x=0$ or $b\cos x-a\sin x = 0$.Either forces $(a,b)$ to vanish somewhere. | |
| Oct 8, 2021 at 9:30 | answer | added | Nicolast | timeline score: 5 | |
| Oct 7, 2021 at 20:44 | answer | added | Pierre PC | timeline score: 3 | |
| Oct 7, 2021 at 13:19 | history | asked | Martim Pereir | CC BY-SA 4.0 |