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Special geometries associated to quaternion-Kähler 8-manifolds. (English) Zbl 1318.53044

Summary: We develop a calculus of differential forms on a quaternion-Kähler manifold \(M^{4 n}\) admitting an isometric circle action. This is used to study three fundamental examples of such actions on the quaternionic projective plane and the construction of \(G_2\) and half-flat structures on quotients of \(M^8\) and its hypersurfaces.

MSC:

53C26 Hyper-Kähler and quaternionic Kähler geometry, “special” geometry
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