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Twistor Bundles of Almost Symplectic Manifolds
Nannicini, Antonella
1998
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.
Series
Rendiconti dell’Istituto di Matematica dell’Università di Trieste. An International Journal of Mathematics
30 (1998)
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 (1998), pp. 45-55.
Languages
en
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