Timeline for Kahler structure on flag manifolds
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
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| Apr 14, 2016 at 14:41 | comment | added | Ben McKay | Clearly no complex manifold admits a finite number of Kähler structures, unless that number is zero, as you can rescale a Kähler metric. | |
| Apr 14, 2016 at 14:39 | history | edited | Ben McKay | CC BY-SA 3.0 |
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| Jul 22, 2013 at 3:58 | comment | added | Francois Ziegler | The quoted paper of Alekseevsky is online here: elib.mi.sanu.ac.rs/pages/browse_issue.php?db=zr&rbr=14 | |
| Jun 25, 2013 at 16:15 | comment | added | Robert Bryant | While the space of $G$-invariant complex structures on the flag manifold is finite, the space of $G$-invariant compatible Kähler structures is only finite dimensional in general, rather than finite. For example, consider the simplest flag variety $F_{1,2} = \mathrm{SU}(3)/\mathbb{T}^2$. The space $S$ of closed, $\mathrm{SU}(3)$-invariant $2$-forms on $F_{1,2}$ has dimension $2$, and, for each of the $\mathrm{SU}(3)$-invariant complex structures $J$, there is an open set $S_J\subset S$ that consists of Kähler forms compatible with $J$. | |
| Mar 21, 2012 at 20:05 | vote | accept | Dyke Acland | ||
| Mar 9, 2012 at 14:34 | history | answered | 314159. | CC BY-SA 3.0 |