Timeline for Is the cotangent bundle to a Kahler manifold hyperkahler?
Current License: CC BY-SA 2.5
5 events
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| Jul 25, 2017 at 18:17 | comment | added | Ashley | @Sam if you don't mind me asking, what do you mean by the induced metric on $T^*M$ that you mention in your question? The induced complex structure and canonical holomorphic symplectic form I can see (and I know that in general these are not compatible, so your metric is not coming from these two). Do you mean something like the Sasaki metric on $TM$ transferred to $T^*M$ or am i way over complicating things? Thanks! | |
| Nov 20, 2010 at 18:38 | vote | accept | Sam Gunningham | ||
| Nov 20, 2010 at 17:42 | answer | added | Tony Pantev | timeline score: 16 | |
| Nov 20, 2010 at 17:29 | comment | added | José Figueroa-O'Farrill | I don't think that this is true in general. There are special cases where this is true, though. I think that if $M$ is a generalised flag manifold then yes, by results of Nakajima and also Biquard. Similarly if $M$ is a noncompact hermitian symmetric space, by results of Biquard and Gauduchon. There is also work of Kronheimer showing that there is a hyperkähler metric on the cotangent bundle of a complexified Lie group. | |
| Nov 20, 2010 at 17:13 | history | asked | Sam Gunningham | CC BY-SA 2.5 |