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Twistor theory of symplectic manifolds
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UNSPECIFIED (2006) Twistor theory of symplectic manifolds. JOURNAL OF GEOMETRY AND PHYSICS, 56 (2). pp. 214-246. doi:10.1016/j.geomphys.2005.01.007
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Official URL: http://dx.doi.org/10.1016/j.geomphys.2005.01.007
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. (c) 2004 Elsevier B.V. All rights reserved.
| Item Type: | Journal Article | ||||
|---|---|---|---|---|---|
| Subjects: | Q Science > QA Mathematics Q Science > QC Physics |
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| Journal or Publication Title: | JOURNAL OF GEOMETRY AND PHYSICS | ||||
| Publisher: | ELSEVIER SCIENCE BV | ||||
| ISSN: | 0393-0440 | ||||
| Official Date: | February 2006 | ||||
| Dates: |
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| Volume: | 56 | ||||
| Number: | 2 | ||||
| Number of Pages: | 33 | ||||
| Page Range: | pp. 214-246 | ||||
| DOI: | 10.1016/j.geomphys.2005.01.007 | ||||
| Publication Status: | Published |
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