OpenstarTs >
EUT-Periodici >
Rendiconti dell’Istituto di matematica dell’Università di Trieste: an International Journal of Mathematics >
Rendiconti dell' Istituto di matematica dell‘ Università di Trieste: an International Journal of Mathematics vol.34 (2002) >

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
Citation: 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 $Z\left(M,\omega\right)$.
URI: http://hdl.handle.net/10077/4207
ISSN: 0049-4704
MS Classification: 53C26
53C28
53D05
Appears in Collections:Rendiconti dell' Istituto di matematica dell‘ Università di Trieste: an International Journal of Mathematics vol.34 (2002)

Files in This Item:

File Description SizeFormat
NanniciniRendMat34.pdf267.14 kBAdobe PDFView/Open
View Statistics

Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.