HyperKähler and quaternionic Kähler geometry
A (pseudo-) hyperKähler \((4n+4)\)-manifold \({\mathcal U}(M)\) is constructed for each quaternionic Kähler 4n-manifold in a way that is compatible with generalizations of the Marsden-Weinstein symplectic quotient. The manifold \({\mathcal U}(M)\) admits: (1) a certain type of SU(2)-action permuting the complex structures; (2) a function which is a Kähler potential for each complex structure; (3) quaternionic Kähler metrics in the same quaternionic class. Locally (1), (2) and (3) are equivalent and characterize \({\mathcal U}(M)\). Examples include, for a compact semisimple Lie group G, the nilpotent orbits in \({\mathfrak g}^{{\mathbb{C}}}\), which are seen to be fibred over quaternionic Kähler manifolds.
scientific article; zbMATH DE number 4169614
scientific article