Timeline for Developable 3-manifolds in $\mathbb{R}^4$
Current License: CC BY-SA 3.0
7 events
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| Apr 13, 2017 at 12:58 | history | edited | CommunityBot |
replaced http://mathoverflow.net/ with https://mathoverflow.net/
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| Jul 29, 2011 at 21:46 | comment | added | Joseph O'Rourke | @Ryan: Great! Terminological variations are converging... | |
| Jul 29, 2011 at 21:40 | comment | added | Ryan Budney | For 3-manifolds the Riemann curvature tensor is recoverable from the Ricci tensor, so "Ricci flat" implies its a Euclidean manifold -- locally isometric to open subsets of $\mathbb R^3$. | |
| Jul 29, 2011 at 21:09 | history | edited | Will Jagy | CC BY-SA 3.0 |
added 162 characters in body
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| Jul 29, 2011 at 20:52 | comment | added | Joseph O'Rourke | Thanks, Will, I just ordered the Thorpe book. For the record, Hick's Cor.6: "A hypersurface is Ricci flat if and only if it is Einstein with total curvature zero. If $n=3$ and $M$ is Ricci flat, then the second mean curvature is also zero so at points $m$ on $M$ that are not flat points ($L_m \neq 0$), the multiplicity of the nonzero principle curvature is unity." | |
| Jul 29, 2011 at 20:13 | history | edited | Will Jagy | CC BY-SA 3.0 |
added 270 characters in body
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| Jul 29, 2011 at 19:38 | history | answered | Will Jagy | CC BY-SA 3.0 |