Timeline for Negative sectional curvature and constant curvature
Current License: CC BY-SA 4.0
17 events
| when toggle format | what | by | license | comment | |
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| Aug 30, 2021 at 14:05 | history | edited | Stefan Kohl♦ | CC BY-SA 4.0 |
Fixed a number of typos.
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| Aug 30, 2021 at 14:05 | history | made wiki | Post Made Community Wiki by Stefan Kohl♦ | ||
| Sep 20, 2017 at 19:53 | history | edited | coudy | CC BY-SA 3.0 |
typo in title. sectionnal -> sectional
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| Jun 9, 2013 at 8:14 | vote | accept | Selim G | ||
| Jun 8, 2013 at 14:16 | answer | added | Igor Belegradek | timeline score: 19 | |
| Jun 8, 2013 at 10:15 | comment | added | Selim G | Igor : I am mainly interested in propetries of closed manifolds | |
| Jun 8, 2013 at 5:17 | answer | added | Misha | timeline score: 14 | |
| Jun 7, 2013 at 23:49 | comment | added | Misha | Selim: You should also address Igor's question: Are manifolds in your jungle compact or merely complete (or, maybe, of finite volume)? When you edit, you should list topological properties that you know. | |
| Jun 7, 2013 at 23:42 | history | edited | Selim G | CC BY-SA 3.0 |
deleted 489 characters in body
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| Jun 7, 2013 at 23:40 | comment | added | Selim G | Misha : You are right, my question is not specific enough. In the jungle of differentiable manifolds, let's try to locate those which can carry a riemanniann metric of negative sectionnal curvature. It seems that this condition is very restrictive. I would like to understand how much it is. So I think the relevant question is : what are the topological properties which a manifold of variable curvature must have, and in a second time what are the topological properties manifolds of constant curvature have and variable curvature might not have. | |
| Jun 7, 2013 at 18:28 | comment | added | Misha | Now, as the question is rewritten, it makes less sense than before, as you are casting your net way too wide: Are you interested in common topological properties of all closed manifolds admitting metrics of negative curvature? Are you interested in topological properties which manifolds of constant curvature have and variable curvature might not have? Are you interested in geometric properties of metrics of negative curvature? All of these? If so, this is not a good question for MO as it is too unfocused; an "answer" would have to include, say, a survey of hyperbolic groups. | |
| Jun 7, 2013 at 18:14 | comment | added | Misha | See also mathoverflow.net/questions/107716/… | |
| Jun 7, 2013 at 14:39 | history | edited | Selim G | CC BY-SA 3.0 |
added 379 characters in body
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| Jun 7, 2013 at 14:31 | comment | added | Selim G | Yes I know those examples, actually this question arised while studying them. Maybe I should precise my question, because I'm interested in the properties btoh kind of manifolds shares. I realize the way I aked my question is not clear ! | |
| Jun 7, 2013 at 13:52 | comment | added | Benoît Kloeckner | Given the form of the question, it should be community wiki. You should prbobly look at the examples constructed by Gromov of manifolds having metrics of arbitrarily pinched negative curvature, that admit no hyperbolic metric. I do not know more than their existence myself, though. | |
| Jun 7, 2013 at 12:05 | comment | added | Misha | Haagerup property of the fundamental group is one key difference: You have it in constant curvature, but it fails for some negatively curved manifolds. | |
| Jun 7, 2013 at 11:11 | history | asked | Selim G | CC BY-SA 3.0 |