Abstract
In this paper we generalize the definition of symplectic connection to the contact case. It turns out that any odd-dimensional manifold equipped with a contact form admits contact connections and that any Sasakian structure induces a canonical contact connection. Furthermore (as in the symplectic case), any contact connection induces an almost CR structure on the contact twistor space which is integrable if and only if the curvature of the connection is of Ricci-type.
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This work was supported by the Project M.I.U.R. “Riemannian Metrics and Differentiable Manifolds” and by G.N.S.A.G.A. of I.N.d.A.M.
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Vezzoni, L. Connections on contact manifolds and contact twistor space. Isr. J. Math. 178, 253–267 (2010). https://doi.org/10.1007/s11856-010-0065-2
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DOI: https://doi.org/10.1007/s11856-010-0065-2