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Twistor methods in conformal almost symplectic geometry
Nannicini, Antonella
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 $Z\left(M,\omega\right)$.
Series
Rendiconti dell’Istituto di Matematica dell’Università di Trieste. An International Journal of Mathematics
34 (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.
Languages
en
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