Timeline for Almost-geodesics on a Riemannian Hilbert manifold which are still almost geodesics in some submanifold
Current License: CC BY-SA 4.0
13 events
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| Jun 30, 2020 at 13:49 | history | edited | Manuel Norman | CC BY-SA 4.0 |
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| Jun 30, 2020 at 13:46 | comment | added | Manuel Norman | This is a great improvement of the question, thanks! | |
| Jun 30, 2020 at 13:30 | comment | added | Thomas Rot | There are mathematical questions here if you change the quantifiers. For example one can define an $\epsilon$-almost geodesic as a curve that satisfies the bound with the given $\epsilon$. The question is then what submanifolds are $\epsilon$-almost geodesic? Maybe you will need to add some extra conditions on how to make the measurment precise for long geodesics. I would not know the answer (even in the finite dimensional case). | |
| Jun 30, 2020 at 11:07 | comment | added | Manuel Norman | Ah, you're right! I was focusing too much on the theorem and didn't notice this. Thanks! | |
| Jun 30, 2020 at 11:02 | comment | added | Thomas Rot | Any curve is an almost geodesic then. | |
| Jun 30, 2020 at 10:08 | history | edited | Manuel Norman | CC BY-SA 4.0 |
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| Jun 30, 2020 at 10:00 | history | edited | Manuel Norman | CC BY-SA 4.0 |
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| Jun 30, 2020 at 9:52 | comment | added | Manuel Norman | Sure, I will add the definition in the question | |
| Jun 30, 2020 at 9:52 | comment | added | Thomas Rot | can you define the notion of "almost geodesic" for me? | |
| Jun 30, 2020 at 9:46 | history | edited | Manuel Norman | CC BY-SA 4.0 |
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| Jun 30, 2020 at 9:44 | comment | added | Manuel Norman | Yes, you are right, thanks for noting this. Actually, what I'm most interested in now is not the metric used (we just need one for which $H$ is complete, so that almost geodesics certainly exist), but the existence of almost geodesics on $H$ which are still almost geodesics on $M$. Any metric for which this happens will suffice, so we can consider the inner product | |
| Jun 30, 2020 at 9:41 | comment | added | Thomas Rot | About your introduction: $H$ with the Riemannian metric induced by the inner product is itself is a complete Hilbert manifold right? Do you mean to study other complete metrics? | |
| Jun 30, 2020 at 9:32 | history | asked | Manuel Norman | CC BY-SA 4.0 |