Handbook of Pseudo-Riemannian Geometry and Supersymmetry

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pp: 15–37

DOI: 10.4171/079-1/2

Differential forms on quaternionic Kähler manifolds

Gregor Weingart[1]

(1) Universidad Nacional Autónoma de México, Cuernavaca, Mexico

The bundle of differential forms on a hyper-Kähler manifold is a representation of a natural Lie algebra so4,1ℝ of parallel operators. After constructing this algebra from the point of view of representation theory we calculate the minimal parallel decomposition of the bundle of differential forms on hyper-Kähler and quaternionic Kähler manifolds.

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