Please use this identifier to cite or link to this item: http://hdl.handle.net/10077/4360
Title: Twistor Bundles of Almost Symplectic Manifolds
Authors: Nannicini, Antonella
Issue Date: 1999
Publisher: Università degli Studi di Trieste. Dipartimento di Scienze Matematiche
Source: Antonella Nannicini, "Twistor Bundles of Almost Symplectic Manifolds", in: Rendiconti dell’Istituto di Matematica dell’Università di Trieste. An International Journal of Mathematics, 30 (1999), pp. 45-55.
Series/Report no.: Rendiconti dell’Istituto di Matematica dell’Università di Trieste. An International Journal of Mathematics
30 (1999)
Abstract: In this paper we introduce the twistor bundle of a 2n-dimensional almost symplectic manifold M as the quotient bundle $\frac{P\left(M,Sp\left(2n\right)\right)}{U\left(n\right)}$. Given a symplectic connection on M we introduce a natural almost Hermitian structure on the twistor bundle and we prove that this structure is K$\ddot{\textrm{a}}$hler if and only if M is symplectic and the chosen connection has vanishing curvature and (0,2)-part of the torsion. Moreover we prove that in the case of $\mathbb{R}^{2n}$ with standard symplectic structure the twistor bundle turns out to be K$\ddot{\textrm{a}}$hler with constant scalar curvature for a certain class of symplectic connections.
URI: http://hdl.handle.net/10077/4360
ISSN: 0049-4704
Appears in Collections:Rendiconti dell'Istituto di matematica dell'Università di Trieste: an International Journal of Mathematics vol.30 (1999)

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