Hyperk Ahler Structures and Group Actions
نویسندگان
چکیده
منابع مشابه
Invariant Hyperk Ahler Metrics with a Homogeneous Complex Structure
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 ...
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The pairing can be viewed as giving families of invariants of hyperk\"ahler manifolds or as giving families of 3-manifold invariants. In the first approach, one hopes to derive theorems about the geometry of hyperk\"ahler manifolds (this has been initiated by Hitchin and Sawon). In the second approach, the invariants obtained are finite-type invariants, so their computation factorises into two ...
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We study the hyperkk ahler metrics associated to minimal singularities in the nilpotent variety of a semisimple Lie group. We show that Kronheimer's 4-dimensional ALE spaces are naturally realized within the context of coadjoint orbits and can be thought of as certain moduli spaces of SU(2) invariant instantons on R 4 nf0g with appropriate boundary conditions. We also show that the hyperkk ahle...
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