Timeline for Complete statistical manifolds
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Dec 22, 2020 at 21:03 | comment | added | Catologist_who_flies_on_Monday | you're right. I think I misread something. Thanks a lot Gabe K! You've been a big help. | |
| Dec 22, 2020 at 20:03 | comment | added | Gabe K | I'm not sure exactly what the bounds on the sectional curvature are. In particular, I don't see why $K\left(\operatorname{span}\left\{e_{i}, E_{j k}\right\}, P\right)=-\frac{1}{4}\left(2 a_{i j k} \bar{\varrho}_{i j} \bar{\varrho}_{k j} \bar{\rho}_{k i}+\bar{\varrho}_{i j}^{2}+\bar{\varrho}_{i k}^{2}\right) /\left(1+\bar{\varrho}_{j k}^{2}\right)$ is necessarily bounded from below by $-1/2.$ It's definitely possible but not obvious. Also, I don't see how the sectional curvature could ever exceed $1/4$, so you can probably tighten the upper bound. | |
| Dec 22, 2020 at 4:27 | vote | accept | Catologist_who_flies_on_Monday | ||
| Dec 22, 2020 at 4:25 | comment | added | Catologist_who_flies_on_Monday | I'm reading thought the article, but I thought to ask also am I correct in interpreting Theorem 2.2 to imply that this manifold has sectional curvature bounded between $[-\frac1{2},\frac1{2}]$? | |
| Dec 22, 2020 at 4:17 | comment | added | Gabe K | Thanks for the nice question! I'm also interested in seeing what examples are suggested since many common examples of statistical manifolds are incomplete. | |
| Dec 22, 2020 at 4:09 | comment | added | Catologist_who_flies_on_Monday | Thank you very much for the warm welcome and very detailed/interesting post Gabe K. If you don't mind, I'll accept it shortly but I'll wait abit first to see if any other interesting examples trickle in. | |
| Dec 22, 2020 at 3:59 | history | answered | Gabe K | CC BY-SA 4.0 |