Timeline for Riemannian manifolds that are scalar flat but not Ricci flat
Current License: CC BY-SA 4.0
6 events
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| Oct 13, 2020 at 12:48 | history | edited | Bernd Ammann | CC BY-SA 4.0 |
added 10 characters in body
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| Oct 13, 2020 at 12:46 | comment | added | Bernd Ammann | If you are familiar with Ricci flow, the easiest argument to prove "On a compact connected manifold that does not carry a metric of positive scalar curvature, every scalar flat metric is Ricci-flat." is as follows: Assume that $g_t$, $t\in [0,\epsilon)$ is a solution of the Ricci-flow with $g_0$ scalar flat. Then it is a standard results within the theory of Ricci flow, thar either $g_0$ is Ricci-flat (and thus $g_0=g_t$ for all $t$) or $g_t$ has positive scalar curvature for all $t>0$. A proof of his should be contained in every advanced textbook on Ricci flow. | |
| Apr 11, 2020 at 19:03 | comment | added | José Figueroa-O'Farrill | @Bilateral See mathoverflow.net/a/294346/394 | |
| Nov 15, 2018 at 14:01 | comment | added | Bilateral | Could you please give a reference about the statement "On a compact manifold that does not carry a metric of positive scalar curvature, every scalar flat metric is Ricci-flat."? Thanks. | |
| Jun 8, 2017 at 14:02 | history | edited | YCor | CC BY-SA 3.0 |
added missing word
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| Jun 8, 2017 at 12:49 | history | answered | Bernd Ammann | CC BY-SA 3.0 |