Timeline for Riemannian metrics on matrix space for which the restriction of trace function to each complete geodesic is a bounded function
Current License: CC BY-SA 4.0
18 events
| when toggle format | what | by | license | comment | |
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| Jun 11, 2020 at 11:22 | vote | accept | Ali Taghavi | ||
| S Jun 11, 2020 at 11:21 | history | bounty ended | Ali Taghavi | ||
| S Jun 11, 2020 at 11:21 | history | notice removed | Ali Taghavi | ||
| Jun 9, 2020 at 14:39 | answer | added | Gabe K | timeline score: 3 | |
| S Jun 9, 2020 at 9:35 | history | bounty started | Ali Taghavi | ||
| S Jun 9, 2020 at 9:35 | history | notice added | Ali Taghavi | Draw attention | |
| Jun 6, 2020 at 17:02 | history | edited | Ali Taghavi | CC BY-SA 4.0 |
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| Jun 6, 2020 at 15:48 | history | edited | Ali Taghavi | CC BY-SA 4.0 |
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| Jun 6, 2020 at 15:09 | history | edited | Ali Taghavi | CC BY-SA 4.0 |
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| Jun 6, 2020 at 15:04 | history | edited | Ali Taghavi | CC BY-SA 4.0 |
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| Jun 6, 2020 at 14:57 | comment | added | Ali Taghavi | @leomonsaingeon Thank you for your comment. I revise my question. | |
| Jun 6, 2020 at 14:57 | comment | added | leo monsaingeon | right, but the continuity of the trace function depends on the choice of the metric (although I agree that pretty much all the Riemannian structures should give an equivalent topology). So it was not completely clear for me what you meant. Now it is ;-) | |
| Jun 6, 2020 at 14:55 | comment | added | Ali Taghavi | @leomonsaingeon I mean complete geodesic, otherwise not only trace but also every continuous function on a compact set9geoesic from M to N) is a bounded function | |
| Jun 6, 2020 at 14:54 | comment | added | leo monsaingeon | well, not if you mean "geodesics between arbitrary pairs of points", in which case your time parameter cannot run across the whole real line. But I guess from your comment that you really mean "complete geodesics", right? If so perhaps it would be worth editing your question (also, there is a typo in your title "o"->"of") | |
| Jun 6, 2020 at 14:53 | comment | added | Ali Taghavi | @leomonsaingeon I think it is the Eucliean metric so the geodesic $\begin{pmatrix}t&0\\0&0\end{pmatrix}$ has an unbounded trace, right? | |
| Jun 6, 2020 at 14:50 | history | edited | Ali Taghavi | CC BY-SA 4.0 |
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| Jun 6, 2020 at 14:50 | comment | added | leo monsaingeon | Do you mean complete geodesics? Or just two-points geodesics between arbitrary matrices $M,N$? In the latter case the Hilbert structure induced by the Frobenius scalar product should do, right? | |
| Jun 6, 2020 at 14:47 | history | asked | Ali Taghavi | CC BY-SA 4.0 |