Weyl connections and the local sphere theorem for quaternionic contact structures
نویسندگان
چکیده
منابع مشابه
Conformal Quaternionic Contact Curvature and the Local Sphere Theorem
Abstract. A curvature-type tensor invariant called quaternionic contact (qc) conformal curvature is defined on a qc manifolds in terms of the curvature and torsion of the Biquard connection. The discovered tensor is similar to the Weyl conformal curvature in Riemannian geometry and to the Chern-Moser invariant in CR geometry. It is shown that a qc manifold is locally qc conformal to the standar...
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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...
متن کاملQuaternionic 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 (M,Q) defined by D with the space of ∂̄-...
متن کاملQuaternionic Contact Einstein Structures and the Quaternionic Contact Yamabe Problem
A partial solution of the quaternionic contact Yamabe problem on the quaternionic sphere is given. It is shown that the torsion of the Biquard connection vanishes exactly when the trace-free part of the horizontal Ricci tensor of the Biquard connection is zero and this occurs precisely on 3-Sasakian manifolds. All conformal deformations sending the standard flat torsion-free quaternionic contac...
متن کاملConformal Quaternionic Contact Curvature and the Local Sphere Theorem. La Courbure Conforme D’une Structure De Contact Quaternionienne Et Structures Localment Plates
A tensor invariant is defined on a quaternionic contact manifold in terms of the curvature and torsion of the Biquard connection involving derivatives up to third order of the contact form. This tensor, called quaternionic contact conformal curvature, is similar to the Weyl conformal curvature in Riemannian geometry and to the Chern-Moser tensor in CR geometry. It is shown that a quaternionic c...
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ژورنال
عنوان ژورنال: Annals of Global Analysis and Geometry
سال: 2010
ISSN: 0232-704X,1572-9060
DOI: 10.1007/s10455-010-9228-y