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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 ISSN 0393-0440.

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Official URL: http://dx.doi.org/10.1016/j.geomphys.2005.01.007

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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. (c) 2004 Elsevier B.V. All rights reserved.

Item Type: Journal Article
Subjects: Q Science > QA Mathematics
Q Science > QC Physics
Journal or Publication Title: JOURNAL OF GEOMETRY AND PHYSICS
Publisher: ELSEVIER SCIENCE BV
ISSN: 0393-0440
Official Date: February 2006
Dates:
DateEvent
February 2006UNSPECIFIED
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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