Timeline for Homogeneous metric surfaces
Current License: CC BY-SA 4.0
9 events
| when toggle format | what | by | license | comment | |
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| Sep 12, 2020 at 6:22 | comment | added | user44143 | I mentioned this same theorem of Busemann’s at the end of an answer to another question, mathoverflow.net/a/346560. But the taxicab metric shows that Ghys’s first and third hypotheses on their own will not imply Busemann’s axiom for uniqueness of prolongation. | |
| Sep 11, 2020 at 17:09 | comment | added | coudy | @McKay thanks, indeed the two books of buseman contain results pretty close to Ghys'statement, e.g. 55.3 in "geometry of geodesics". I am not sure how Ghys' hypotheses imply axiom IV of Busemann's G-space but the reference to Berestovskii by Igor seems to sort it out. Busemann is citing Tits (1952) for the two-dimensional case but I can't find the article at the moment. | |
| Sep 11, 2020 at 12:10 | comment | added | Igor Belegradek | See theorem 7 in the survey arxiv.org/abs/1412.7893, and also arxiv.org/abs/2007.11917. | |
| Sep 11, 2020 at 10:30 | history | edited | coudy | CC BY-SA 4.0 |
clarification
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| Sep 11, 2020 at 10:29 | comment | added | coudy | @YCor Indeed there are several hyperbolic and spherical spaces, classified up to isometry by the area of their unit disc. And only one euclidean space. So isometric to one of these. | |
| Sep 11, 2020 at 9:02 | comment | added | YCor | It's not true as stated: you should replace "isometric" with "homothetic". | |
| Sep 11, 2020 at 9:01 | history | edited | YCor | CC BY-SA 4.0 |
formatting; edited tags
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| Sep 11, 2020 at 8:22 | comment | added | Ben McKay | I think it is in Busemann's work, either Geometry of Geodesics, or Metric methods in Finsler spaces and in the foundations of geometry | |
| Sep 11, 2020 at 8:16 | history | asked | coudy | CC BY-SA 4.0 |