Timeline for Isometric imbedding of ellipsoidal projective plane
Current License: CC BY-SA 3.0
3 events
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| Aug 29, 2017 at 16:44 | comment | added | Robert Bryant | It might be worth mentioning that it is known that any (smooth) metric on a compact surface can be smoothly isometrically embedded into $\mathbb{R}^5$. (Anton's method below constructs an explicit ellipsoidal metric embedding of $\mathbb{RP}^2$ into $\mathbb{R}^6$.) Meanwhile, it appears still to be unknown whether there is any metric on $\mathbb{RP}^2$ with positive Gauss curvature that can be smoothly isometrically embedded into $\mathbb{R}^4$. Cf., the discussion in M. Gromov's, Partial Differential Relations, Section 3.2.4. | |
| Aug 28, 2017 at 21:11 | answer | added | Anton Petrunin | timeline score: 6 | |
| Aug 24, 2017 at 6:25 | history | asked | Min-Oo | CC BY-SA 3.0 |