Invariant Hyperk Ahler Metrics with a Homogeneous Complex Structure
نویسندگان
چکیده
We give a hyperkk ahler analogue of the classiication of compact homogeneous KK ahler manifolds. Namely we show that, for a compact semisimple Lie group G, the complete G-invariant hyperkk ahler manifolds which are also locally G c-homogeneous with respect to one of the complex structures are precisely the hy-perkk ahler metrics of Kronheimer, Biquard and Kovalev on coadjoint semisimple orbits of G c. As a consequence the only complete hyperkk ahler metrics which are of cohomo-geneity one with respect to a triholomorphic action of compact semisimple Lie group are the at metric on H n and the Calabi metric on T C P n .
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