Timeline for Nash embedding theorem for 2D manifolds
Current License: CC BY-SA 2.5
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Sep 8, 2010 at 1:11 | comment | added | Deane Yang | Will, I am unaware of any particularly nice isometric embeddings of complete hyperbolic surfaces in a higher dimensional Euclidean space. Even the hyperbolic plane is problematic. The best isometric embedding of the hyperbolic plane I know is into 2+1 Minkowski space. | |
| Sep 7, 2010 at 23:26 | comment | added | Will Jagy | Actually, some nice embedding in $S^k$ or $H^k$ would also be more than I know at the moment. | |
| Sep 7, 2010 at 23:25 | comment | added | Will Jagy | Dear Prof. Yang, There are preferred isometric embeddings for the 2-sphere in $R^3 $ as the round sphere, the flat Clifford torus in $R^4$. Ignoring the idea of best possible dimension, are there preferred isometric embeddings of the oriented higher genus constant curvature compact surfaces in $R^k$? Here the concept of "preferred" could mean anything appropriate. Will. | |
| Sep 7, 2010 at 1:46 | vote | accept | CommunityBot | ||
| Sep 7, 2010 at 1:46 | |||||
| Sep 4, 2010 at 14:32 | comment | added | Joseph O'Rourke | Yes, thanks, the $R^5$ result must be as you say in here: Gromov, M. Partial Differential Relations, Springer-Verlag, Ergeb. der Math. 3 Folge, Bd. 9, Berlin-Heidelberg-New-York, 1986. I don't have that book. It would be useful to have a precise reference. | |
| Sep 4, 2010 at 14:04 | history | answered | Deane Yang | CC BY-SA 2.5 |