Timeline for Large geodesically convex subsets of tori
Current License: CC BY-SA 3.0
4 events
| when toggle format | what | by | license | comment | |
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| Jan 17, 2012 at 3:36 | comment | added | Will Jagy | Nikita, take any line through the origin with rational slope, so $y = \frac{m}{n} \; x.$ This line also passes through the lattice point $(n,m).$ This point is identified with the origin in the torus you define, so it is a closed curve. For example, the line $y = x$ is a closed geodesic in the torus. It is instructive to draw the image of, say, $y = \frac{5}{3} \; x$ in the original 1 by 1 square under identification. | |
| Jan 17, 2012 at 2:29 | comment | added | Nikita Sidorov | Sorry, don't understand it, starting with 3. Geodesic circles are either vertical or horizontal, aren't they? So, what do you mean by `slope'? With a slope geodesics will not be even closed. | |
| Jan 16, 2012 at 23:22 | history | edited | Zarathustra | CC BY-SA 3.0 |
added 6 characters in body; added 21 characters in body
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| Jan 16, 2012 at 23:09 | history | answered | Zarathustra | CC BY-SA 3.0 |