Timeline for Nash embedding theorem for 2D manifolds
Current License: CC BY-SA 2.5
6 events
| when toggle format | what | by | license | comment | |
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| Sep 4, 2010 at 13:56 | vote | accept | CommunityBot | ||
| Sep 4, 2010 at 13:56 | |||||
| Sep 4, 2010 at 12:49 | comment | added | Joseph O'Rourke | @Jose: Yes, what you say holds in the smooth category. I guess that was implied; sorry. So consider my comment just a remark that without that assumption, the situation alters. | |
| Sep 4, 2010 at 12:46 | history | edited | José Figueroa-O'Farrill | CC BY-SA 2.5 |
added 11 characters in body
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| Sep 4, 2010 at 12:42 | comment | added | José Figueroa-O'Farrill | @Joseph: Guilty as charged! But aren't we in the smooth category? At least that is what I understood from the way the question was phrased. | |
| Sep 4, 2010 at 12:19 | comment | added | Joseph O'Rourke | @Jose: I believe your statement is correct only with the additional qualification that the embedding is smooth? Zalgaller has constructed an isometric embedding of the flat torus. See my answer to this MO question: mathoverflow.net/questions/31222/… . I think in your proof sketch the conclusion that the curvatures agree at the contact point requires the embedding to be smooth. | |
| Sep 4, 2010 at 11:21 | history | answered | José Figueroa-O'Farrill | CC BY-SA 2.5 |