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 Mathematics
34 (2002)
Abstract: 
Given a 2n-dimensional almost symplectic manifold $\left(M,\omega\right)$,
we consider the conformal class of $\omega$ and to each symplectic
connection, $\nabla$, we associate, in a natural way, a $e^{2\sigma}\omega$-symplectic
connection, $\nabla^{\sigma}$. 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 trough
the existence of special symplectic connections. Finally we prove
that, in the case of a special K$\ddot{\textrm{a}}$hler manifold,
the section of $Z\left(M,\omega\right)$ defined by the complex structure
of M is an almost complex submanifold with respect to a certain almost
complex 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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