Timeline for Converse to Euclid's fifth postulate
Current License: CC BY-SA 3.0
16 events
| when toggle format | what | by | license | comment | |
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| Jan 27, 2021 at 18:12 | comment | added | Moishe Kohan | In the case of metrics of nonpositive curvature, this question is due to Keith Burns, and, I think, it is still open. You may want to ask Keith directly if he knows of any progress in this direction. | |
| Jan 27, 2021 at 16:28 | answer | added | Nicolast | timeline score: 6 | |
| Jun 16, 2019 at 20:26 | comment | added | Sylvain JULIEN | Could Nash's isometric embedding theorem provide a counter-example? | |
| Oct 18, 2017 at 12:36 | comment | added | Mohammad Ghomi | Hi Richard. No assumption is made other than those mentioned above. I do not think that smoothing the cone is going to work, since all asymptotically flat surfaces appear to be OK according to the recent paper of Ge, Guijarro, and Solorzano mentioned above. | |
| Oct 18, 2017 at 5:04 | comment | added | Richard Montgomery | Cones over circles of radius 1/2 or less come close to doing what you want -but the complete geodesics must be stopped when they hit the cone point since they fail to minimize past the cone point. Have you thought of trying to make Riemannian metric counterexamples by smoothing out the cone point of such metrics? | |
| Oct 18, 2017 at 4:57 | comment | added | Richard Montgomery | Dear Mohammad: I take it you do not want to assume any of the other four postulates -- thus the geometry need not be homogeneous or isotropic. Correct? | |
| Oct 15, 2017 at 14:24 | comment | added | Ali Taghavi | I thank you and Wojowu for your comment on my answer to this question. Your comment helped me to realize my answer was not relevant. So I deleted it. | |
| Oct 15, 2017 at 14:16 | comment | added | Ali Taghavi | The answer is yes for those Riemannian steucture which satisfy the equivalency of Pythagoras theorem and 5th postulate. Please see this mathforum post: mathforum.org/kb/message.jspa?messageID=3545911 | |
| Oct 15, 2017 at 13:30 | history | edited | Mohammad Ghomi |
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| Oct 15, 2017 at 3:20 | history | edited | Mohammad Ghomi | CC BY-SA 3.0 |
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| S Oct 14, 2017 at 16:57 | history | suggested | CommunityBot | CC BY-SA 3.0 |
Corrected one typo.
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| Oct 14, 2017 at 16:56 | review | Suggested edits | |||
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| Oct 14, 2017 at 15:33 | history | edited | Mohammad Ghomi | CC BY-SA 3.0 |
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| Oct 14, 2017 at 15:11 | history | edited | Mohammad Ghomi | CC BY-SA 3.0 |
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| Oct 14, 2017 at 15:04 | history | asked | Mohammad Ghomi | CC BY-SA 3.0 |