Talk:Ricci-flat manifold
Latest comment: 2 years ago by Gumshoe2 in topic Plain flatness
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Ricci Flatness edit
Can Ricci flatness redirect here? — Preceding unsigned comment added by 70.247.173.205 (talk) 20:19, 26 February 2016 (UTC)
- Might it be better to merge this article into the one on Ricci curvature? — Cheers, Steelpillow (Talk) 06:54, 23 September 2018 (UTC)
Plain flatness edit
Is there a simple example of how Ricci flatness differs from ordinary flatness? For example can one have a manifold that is not a flat manifold but is Ricci flat, or vice versa? — Cheers, Steelpillow (Talk) 06:46, 23 September 2018 (UTC)
- The Schwarzschild metric illustrated this possibility for Lorentzian metrics. Yau's solution of the Calabi conjecture showed that there are many compact Ricci-flat manifolds which are not flat. Part of the significance of his work was that (as far as I know) it was not known if such examples exist. So it is not easy to come by examples. Gumshoe2 (talk) 07:41, 18 February 2022 (UTC)