Timeline for Length spectrum for Riemannian metrics in the projective plane
Current License: CC BY-SA 3.0
13 events
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| Apr 13, 2017 at 12:58 | history | edited | CommunityBot |
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| Sep 4, 2013 at 8:16 | vote | accept | alvarezpaiva | ||
| Sep 3, 2013 at 9:13 | history | edited | Ricardo Andrade | CC BY-SA 3.0 |
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| Sep 3, 2013 at 8:52 | answer | added | Vladimir S Matveev | timeline score: 5 | |
| Mar 9, 2012 at 2:40 | comment | added | Anton Petrunin | If it is isospectral to the canonical metric then it is isometric. | |
| Mar 8, 2012 at 22:35 | history | edited | alvarezpaiva | CC BY-SA 3.0 |
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| Mar 8, 2012 at 22:28 | history | edited | alvarezpaiva | CC BY-SA 3.0 |
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| Mar 8, 2012 at 22:12 | comment | added | alvarezpaiva | There seem to be various notions that go under the name "length spectrum". The simplest, that I've also seen called the length set is simply the set of lengths of periodic geodesics. One may want to record multiplicities and then you get the multiset that Joseph mentioned in his remark. For my question, I'd be quite happy to know if there are examples of non-isometric Riemannian metrics on the projective plane with the same length set. | |
| Mar 8, 2012 at 21:56 | comment | added | Joseph O'Rourke | @Dmitri: My understanding is that it is the multiset of the lengths of the closed geodesics: list all the lengths of those geodesics, sort them, and record how many times a length is repeated. A variation is the simple length spectrum, the multiset of the lengths of the simple closed geodesics. | |
| Mar 8, 2012 at 21:30 | comment | added | Dmitri Panov | Would you please remind what is length spectrum? | |
| Mar 8, 2012 at 18:03 | history | edited | alvarezpaiva | CC BY-SA 3.0 |
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| Mar 8, 2012 at 17:55 | history | edited | alvarezpaiva | CC BY-SA 3.0 |
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| Mar 8, 2012 at 17:49 | history | asked | alvarezpaiva | CC BY-SA 3.0 |