Quaternionic connections, induced holomorphic structures and a vanishing theorem


We classify the holomorphic structures of the tangent vertical bundle Θ of the twistor fibration of a quaternionic manifold (M,Q) of dimension 4n ≥ 8. In particular, we show that any self-dual quaternionic connection D of (M,Q) induces an holomorphic structure ∂̄ on Θ. We construct a Penrose transform which identifies solutions of the Penrose operator P on… (More)


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