Timeline for Homogenous structure on $S^2\times S^2$ and its geometry
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 10, 2017 at 18:31 | comment | added | Llohann | You can use the compact version $SO(4)/S(O(2)\times O(2))$ (or something like that). people.sju.edu/~ktapp/so4.pdf gives a nice account on left-invariant metrics on $SO(4)$. On the other hand, I am pretty sure that homogeneous manifolds with positive curvature are already classified (please look at Ziller or Wilking survey on positively curved manifolds). | |
| Apr 10, 2017 at 18:14 | comment | added | L.F. Cavenaghi | Nice! Do you know any article that provides the search for $G$-invariants metrics in this space? | |
| Apr 10, 2017 at 18:07 | comment | added | Bombyx mori | @MikhailBorovoi: See math.stackexchange.com/questions/1828484/…, for example. You might find Qiaochu's answer easier to read than mine: math.stackexchange.com/questions/219100/… | |
| Apr 10, 2017 at 16:37 | comment | added | Mikhail Borovoi | Could you please explain here how you construct a bijection between $S^2\times S^2$ and the set of oriented 2-planes in $\mathbb R^4$ ? | |
| Apr 10, 2017 at 16:00 | comment | added | Ben McKay | But the maximal compact subgroup is $PSO(4)=SO(3) \times SO(3)$, preserving the splitting, if I remember correctly. | |
| Apr 10, 2017 at 15:55 | comment | added | Ben McKay | See arxiv.org/pdf/math/0101017.pdf p. 5 for details. | |
| Apr 10, 2017 at 15:53 | history | answered | Ben McKay | CC BY-SA 3.0 |