Quaternionic connections, induced holomorphic structures and a vanishing theorem
نویسنده
چکیده
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 (M,Q) defined by D with the space of ∂̄-holomorphic purely imaginary sections of Θ. We prove that the tensor powers Θ (for any s ∈ N \ {0}) have no global non-trivial ∂̄-holomorphic sections, when (M,Q) is compact and has a compatible quaternionic-Kähler metric of negative (respectively, zero) scalar curvature and the quaternionic connection D is closed (respectively, closed but not exact). 1
منابع مشابه
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. Using a Penrose transform we show that, when (M, Q) is compact and admits a compatible quaternionic-Kähler metric of negative scalar curvature, Θ admits no global non-trivial holomorphic sections with respect to any of its holomorphic structures...
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