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Twistor theory of symplectic manifolds

R. Albuquerque·J. Rawnsley
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Abstract

This article is a contribution to the understanding of the geometry of the twistor space of a symplectic manifold. We consider the bundle $Z$ with fibre the Siegel domain Sp(2n,R)/U(n) existing over any given symplectic 2n-manifold M. Then, after recalling the construction of the almost complex structure induced on $Z$ by a symplectic connection on M, we study and find some specific properties of both. We show a few examples of twistor spaces, develop the interplay with the symplectomorphisms of M, find some results about a natural almost Hermitian structure on $Z$ and finally prove its n+1-holomorphic completeness. We end by proving a vanishing theorem about the Penrose transform.

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BibTeXRIS

R. Albuquerque, J. Rawnsley. 2004-05-27. Twistor theory of symplectic manifolds. https://doi.org/10.1016/j.geomphys.2005.01.007

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