Timeline for Is the cotangent bundle to a Kahler manifold hyperkahler?
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| Dec 4, 2010 at 19:27 | comment | added | Simon Salamon | This answer is pretty complete, but it is worth reading the paper of Calabi in Ann. Ec. Norm. Sup. 12 (1979) for an explicit construction of the HK metric on the cotangent bundle of complex projective space. The precise form of the metric is not obvious, and his approach (subsequently generalized to other HSS's) was to find the Kaehler potential. As in applications of Yau's theorem in the compact case, the HK metric is indeed compatible with the underlying holomorphic symplectic structure. | |
| Nov 20, 2010 at 18:38 | vote | accept | Sam Gunningham | ||
| Nov 20, 2010 at 17:59 | comment | added | Sam Gunningham | Thanks! I might have noticed Kaledin's paper if I searched for "Kaehler" instead of "Kahler"... | |
| Nov 20, 2010 at 17:42 | history | answered | Tony Pantev | CC BY-SA 2.5 |