Please use this identifier to cite or link to this item: http://hdl.handle.net/10077/4207
 Title: Twistor methods in conformal almost symplectic geometry Authors: Nannicini, Antonella Issue Date: 2002 Publisher: Università degli Studi di Trieste. Dipartimento di Scienze Matematiche Source: Antonella Nannicini, "Twistor methods in conformal almost symplectic geometry", in: Rendiconti dell’Istituto di Matematica dell’Università di Trieste. An International Journal of Mathematics, 34 (2002), pp. 215-234. Series/Report no.: Rendiconti dell’Istituto di Matematica dell’Università di Trieste. An International Journal of Mathematics34 (2002) Abstract: Given a 2n-dimensional almost symplectic manifold $\left(M,\omega\right)$,we consider the conformal class of $\omega$ and to each symplecticconnection, $\nabla$, we associate, in a natural way, a $e^{2\sigma}\omega$-symplecticconnection, $\nabla^{\sigma}$. We prove that the twistor bundle $Z\left(M,\omega\right):=\frac{P\left(M,Sp\left(2n\right)\right)}{U(n)}$,with its canonical almost complex structure induced by $\nabla$,is an invariant of the conformal class of $\left(\omega,\nabla\right)$.Then we study the interplay between conformal properties of $\left(M,\omega\right)$and complex properties of $Z\left(M,\omega\right)$, passing troughthe existence of special symplectic connections. Finally we provethat, in the case of a special K$\ddot{\textrm{a}}$hler manifold,the section of $Z\left(M,\omega\right)$ defined by the complex structureof M is an almost complex submanifold with respect to a certain almostcomplex structure on $Z\left(M,\omega\right)$. Type: Article URI: http://hdl.handle.net/10077/4207 ISSN: 0049-4704 Appears in Collections: Rendiconti dell'Istituto di Matematica dell'Università di Trieste: an International Journal of Mathematics vol.34 (2002)

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