Timeline for Hyperkähler structure on $TS^2$
Current License: CC BY-SA 3.0
9 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Aug 23, 2016 at 0:34 | vote | accept | sgvl | ||
| Aug 21, 2016 at 22:34 | comment | added | Qfwfq | "on the hyperkähler manifold $TS^2$ (or $TRP^2$)" - You are not suggesting that you think the real projective plane is diffeomorphic to $S^2$, are you? | |
| Aug 21, 2016 at 21:23 | answer | added | Robert Bryant | timeline score: 5 | |
| Aug 20, 2016 at 14:09 | comment | added | sgvl | @RobertBryant: Thank you very much, this could be useful for my purposes. I have also another related question: I use the (real) coordinates $(x_1,x_2,α_1,α_2)$ since they are usual for Radon's transform. However, one often uses the (complex) Donaldson parameters $a_0,a_1,b_0$ verifying $a_0^2+b_0a_1^2=1.$ How are they related? | |
| Aug 20, 2016 at 13:17 | history | edited | Michael Hardy | CC BY-SA 3.0 |
edited body; edited title
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| Aug 19, 2016 at 8:51 | comment | added | Robert Bryant | Explicit formulae for the operators in coordinates could be somewhat ungainly, especially since there are no global coordinates. Usually, the most useful way of specifying $I$, $J$, and $K$ on a hyperKähler manifold is to specify the three corresponding parallel $2$-forms in some manner. Would that be useful for your purposes? They aren't hard to describe in this particular case, and, once you know them, if you really want the operators themselves, it's just multivariable calculus to write them down in coordinates, given the $2$-forms. If the $2$-forms would be useful to you, let me know. | |
| Aug 17, 2016 at 19:40 | comment | added | მამუკა ჯიბლაძე | I think you could use the fact that the total space of the unit sphere bundle of $TS^2$ is $S^3$. I think. | |
| Aug 17, 2016 at 17:29 | review | First posts | |||
| Aug 17, 2016 at 17:45 | |||||
| Aug 17, 2016 at 17:26 | history | asked | sgvl | CC BY-SA 3.0 |